Difference between revisions of "Research"
(→Computing with Random Bit Streams) (Tag: Visual edit) 

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"''You see things; and you say, 'Why?' But I dream things that never were; and I say, 'Why not?'"––'' '''George Bernard Shaw''' (1856 –1950)  "''You see things; and you say, 'Why?' But I dream things that never were; and I say, 'Why not?'"––'' '''George Bernard Shaw''' (1856 –1950)  
−  Our research spans different disciplines ranging from digital circuit design, to algorithms, to mathematics, to synthetic biology. It tends to be ''inductive'' (as opposed to ''deductive'') and ''conceptual'' (as opposed to ''applied''). A recurring theme is building systems that compute in novel ways with  +  Our research spans different disciplines ranging from digital circuit design, to algorithms, to mathematics, to synthetic biology. It tends to be ''inductive'' (as opposed to ''deductive'') and ''conceptual'' (as opposed to ''applied''). A recurring theme is building systems that compute in novel or unexpected ways with new and emerging technologies. Often, the task of ''analyzing'' the way things work in a new technology is straightforward; however the task of ''synthesizing'' new computational constructs is more challenging. 
−  ==Computing with  +  ==Computing with Random Bit Streams== 
−  +  "''To invent, all you need is a pile of junk and a good imagination.''" –– '''Thomas A. Edison''' (1847–1931)  
−  +  Humans are accustomed to counting in a positional number system – [http://en.wikipedia.org/wiki/Decimal decimal] radix. Nearly all computer systems operate on another positional number system – [http://en.wikipedia.org/wiki/Binary_numeral_system binary] radix. From the standpoint of ''representation'', such positional systems are compact: given a radix ''b'', one can represent ''b<sup>n</sup>'' distinct numbers with ''n'' digits. However, from the standpoint of ''computation'', positional systems impose a burden: for each operation such as addition or multiplication, the signal must be "''decoded''", with each digit weighted according to its position. The result must be "''encoded''" back in positional form. Any student who has designed a [http://en.wikipedia.org/wiki/Binary_multiplier binary multiplier] in a course on [[EE2301  logic design]] can appreciate all the complexity that goes into wiring up such an operation.  
−  [http://  
−  +  ==== Logic that Operates on Probabilities ====  
+  
+  We advocate an alternative representation: random bit streams where the signal value is encoded by the probability of obtaining a one versus a zero. This representation is much less compact than binary radix. However, complex operations can be performed with very simple logic. For instance, multiplication can be performed with a single AND gate; scaled addition can be performed with a multiplexer (MUX).  
{ align="center"  { align="center"  
−  +   [[Image:stochasticmultiplier.pngcenterthumb350px'''Multiplication''' with an AND gate. Here the variables represents the ''probabilities'' of obtaining a 1 versus a 0 in stochastic bit streams. The AND gate produces an output probability <math>c</math> that is the product of the of the input probabilities <math>a</math> and <math>b</math>.]]  
    
−  [[Image:  +   [[Image:stochasticadder.pngthumb320px'''Scaled addition''' with a multiplexer (MUX). 
+  Given input probabilities <math>a</math>, <math>b</math> and <math>s</math>, the MUX produces an output probability <math>c = a s + (1  s) b</math>.]]  
}  }  
−  +  We have developed a general method for synthesizing digital circuitry that computes on such stochastic bit streams. Our method can be used to synthesize arbitrary polynomial functions. Through polynomial approximations, it can also be used to synthesize nonpolynomial functions. Because the representation is uniform, with all bits weighted equally, the resulting circuits are highly tolerant of [http://en.wikipedia.org/wiki/Soft_error soft errors] (i.e., bit flips).  
−  
−  We have developed a  
−  
{  {  
−    +   
{ style="background:#F0E68C"  { style="background:#F0E68C"  
 valign="top"   valign="top"  
 width="100"  '''title''':   width="100"  '''title''':  
−   width="500"  [[Media:  +   width="500"  [[Media:Qian_Riedel_Synthesizing_Logical_Computation_on_Stochastic_Bit_Streams.pdf  Synthesizing Logical Computation on Stochastic Bit Streams]] 
−   valign="top"  +   valign="top" 
 '''authors''':   '''authors''':  
−   [[  +   [[Weikang Qian]] and [[Marc Riedel]] 
 valign="top"   valign="top"  
−   '''  +   '''appeared as''': 
−    +   Techincal Report, UMN 
 valign="top"   valign="top"  
−  
−  
−  
−  
−  
}  }  
−   align=center width="70"   +   align="center" width="70"  
<span class="plainlinks">  <span class="plainlinks">  
−  [http://  +  [http://cadbio.com/wiki/images/6/64/Qian_Riedel_Synthesizing_Logical_Computation_on_Stochastic_Bit_Streams.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> 
−  <br> [  +  <br> 
−   align=center width="70"   +  [[Media:Qian_Riedel_Synthesizing_Logical_Computation_on_Stochastic_Bit_Streams.pdf  Paper]] 
−  <span class="plainlinks">  +   align="center" width="70"  
−  [http://mriedel.ece.umn.edu/  +  <span class="plainlinks">[http://mriedel.ece.umn.edu/files/Riedel_Synthesizing_Logical_Computation_on_Stochastic_Bit_Streams.pptx http://mriedel.ece.umn.edu/wiki/images/3/36/Ppt.jpg]</span> 
−  <br> [http://mriedel.ece.umn.edu/  +  <br>[http://mriedel.ece.umn.edu/files/Riedel_Synthesizing_Logical_Computation_on_Stochastic_Bit_Streams.pptx Slides] 
}  }  
−  
−  
−  
−  
−  
−  
−  
{  {  
    
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 valign="top"   valign="top"  
 width="100"  '''title''':   width="100"  '''title''':  
−   width="500"  [[Media:  +   width="500"  [[Media:Li_Lilja_Qian_Riedel_Bazargan_Logical_Computation_on_Stochastic_Bit_Streams_with_Linear_Finite_State_Machines.pdf  Logical Computation on Stochastic Bit Streams with Linear Finite State Machines]] 
 valign="top"   valign="top"  
 '''authors''':   '''authors''':  
−    +   [http://www.ece.umn.edu/~lipeng/ Peng Li], [http://www.arctic.umn.edu/lilja.shtml David Lilja], [[Weikang Qian]],[http://www.ece.umn.edu/users/kia/ Kia Bazargan] and [[Marc Riedel]] 
−   valign="top"  +   valign="top" 
+   '''appeared in''':  
+   [http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6307798 IEEE Transactions on Computers], Vol. 63, No. 6., pp. 1474–1486, 2014  
+   valign="top"  
 '''presented at''':   '''presented at''':  
−   [http://  +   [http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6165056 IEEE/ACM Asia and South Pacific Design Automation Conference],<br>Sydney, Australia, 2012 
}  }  
−   align=center width="70"   +   align="center" width="70"  
<span class="plainlinks">  <span class="plainlinks">  
−  [http://cctbio.ece.umn.edu/wiki/images/  +  [http://cctbio.ece.umn.edu/wiki/images/7/7c/Li_Lilja_Qian_Riedel_Bazargan_Logical_Computation_on_Stochastic_Bit_Streams_with_Linear_Finite_State_Machines.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> 
−  <br> [  +  <br> 
−  +  [[Media:Li_Lilja_Qian_Riedel_Bazargan_Logical_Computation_on_Stochastic_Bit_Streams_with_Linear_Finite_State_Machines.pdf  Paper]]  
−  
−  
}  }  
−  ====  +  ====Logic that Generates Probabilities==== 
−  +  Schemes for probabilistic computation can exploit physical sources to generate random values in the form of bit streams. Generally, each source has a fixed bias and so provides bits that have a specific probability of being one versus zero. If many different probability values are required, it can be difficult or expensive to generate all of these directly from physical sources. In this work, we demonstrate novel techniques for synthesizing combinational logic that transforms a set of ''source'' probabilities into different ''target'' probabilities.  
+  <!The problem I consider is: given a set ''S'' of ''n'' probabilistic inputs with probabilities ''p''<sub>1</sub>, ..., ''p''<sub><I>n</I></sub> of being one and a target probability ''q'', how can we synthesize a combinational circuit that takes inputs from the set ''S'' and produces an output with probability ''q'' of being one?>  
−  [[  +  [[File:Generate_Probabilities_Example.pngcenterframeGiven a set ''S'' of source probabilities {0.4, 0.5}, we can synthesize a combinational circuit to generate an arbitrary ''decimal'' output probability. The example shows how to generate 0.119. Each AND gate performs a multiplication and each inverter performs a "oneminus" operation.]] 
{  {  
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 valign="top"   valign="top"  
 width="100"  '''title''':   width="100"  '''title''':  
−   width="500"  [[Media:  +   width="500"  [[Media:Qian_Riedel_Zhou_Bruck_Transforming_Probabilities_with_Combinational_Logic.pdf  Transforming Probabilities with Combinational Logic]] 
−   valign="top"  +   valign="top" 
 '''authors''':   '''authors''':  
−   [[  +   [[Weikang Qian]], [[Marc Riedel]], [http://paradise.caltech.edu/~hzhou/ Hongchao Zhou], and [http://paradise.caltech.edu/bruck.html Jehoshua Bruck] 
+   valign="top"  
+   '''will appear in''':  
+   [http://tcad.polito.it/ IEEE Trans. on ComputerAided Design of Integrated Circuits and Systems], 2012.  
 valign="top"   valign="top"  
−   '''  +   '''presented at''': 
−   [http://  +   [http://www.iccad.com/events/eventdetails.aspx?id=1065C International Conference on ComputerAided Design], San Jose, 2009<br>(nominated for '''IEEE/ACM William J. McCalla ICCAD Best Paper Award'''). 
}  }  
−   align=center width="70"   +   align="center" width="70"  
<span class="plainlinks">  <span class="plainlinks">  
−  [http://  +  [http://cadbio.com/wiki/images/d/db/Qian_Riedel_Zhou_Bruck_Transforming_Probabilities_with_Combinational_Logic.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> 
−  <br> [  +  <br> 
−   align=center width="70"   +  [[Media:Qian_Riedel_Zhou_Bruck_Transforming_Probabilities_with_Combinational_Logic.pdf  Paper]] 
−  <span class="plainlinks">[http://  +   align="center" width="70"  
−  <br> [http://  +  <span class="plainlinks">[http://mriedel.ece.umn.edu/files/Qian_Riedel_Bazargan_Lilja_The_Synthesis_of_Combinational_Logic_to_Generate_Probabilities.ppt http://mriedel.ece.umn.edu/wiki/images/3/36/Ppt.jpg]</span> 
+  <br> [http://mriedel.ece.umn.edu/files/Qian_Riedel_Bazargan_Lilja_The_Synthesis_of_Combinational_Logic_to_Generate_Probabilities.ppt Slides]  
}  }  
−  ==Computing with  +  ====Computing with Crappy Clocks==== 
−  "  +  Clock distribution networks are a significant source of power consumption and a major design bottleneck for highperformance circuits. We have proposed a radically new approach: splitting clock domains at a very fine level, with domains consisting of only a handful of gates each. These domains are synchrnonized by "crappy clocks", generated locally with inverter rings. This is feasible if one adopts the paradigm of computing on randomized bit streams. 
+  [[File:polysynchronousand.pngcenterframethumbStochastic multiplication using an AND gate with unsynchronized random bit streams. The stochastic paradigm can tolerate arbitrarly high clock skew. Accordingly, one can replace an expensive global clock distribution network with cheap local clocks, generated by inverter rings – "crappy clocks".]]  
+  {  
+    
+  { style="background:#F0E68C"  
+   valign="top"  
+   width="100"  '''title''':  
+   width="500"  [[Media: Najafi_Lilja_Riedel_Bazargan_Polysynchronous_Stochastic_Circuits.pdf  Polysynchronous Stochastic Circuits]]  
+   valign="top"  
+   '''authors''':  
+   [[M. Hassan_Najafi]], [http://www.arctic.umn.edu/lilja.shtml David Lilja], [[Marc Riedel]], and [http://www.ece.umn.edu/users/kia/ Kia Bazargan]  
+   valign="top"  
+   '''to appear in''':  
+   [http://www.amsv.umac.mo/aspdac2016/ IEEE/ACM Asia and South Pacific Design Automation Conference], 2016  
+  }  
+   align="center" width="70"   
+  <span class="plainlinks">  
+  [http://cctbio.ece.umn.edu/wiki/images/e/ec/Najafi_Lilja_Riedel_Bazargan_Polysynchronous_Stochastic_Circuits.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span>  
+  <br>  
+  [[Media:Najafi_Lilja_Riedel_Bazargan_Polysynchronous_Stochastic_Circuits.pdf  Paper]]  
+  }  
−  +  Please see our "[[Papers,_Theses,_and_Presentations Publications]]" page for more of our papers on these topics.  
−  ==  +  ==Computing with Molecules== 
−  +  “''If I can’t create it, I don’t understand it.''” –– '''Richard Feynman''' (1918–1988)  
+  The theory of [http://en.wikipedia.org/wiki/Chemical_kinetics massaction kinetics] underpins our understanding of biological and chemical systems. It is a simple and elegant formalism: molecular reactions define ''rules'' according to which reactants form products; each rule fires at a ''rate'' that is proportional to the quantities of the corresponding reactants that are present. Just as electronic systems implement computation in terms of '''voltage''' (''energy per unit charge''), we can conceive of molecular systems that compute in terms of '''chemical concentrations''' (''molecules per unit volume''). We are studying techniques for implementing a variety of computational constructs with molecular reactions such as logic, memory, arithmetic, and signal processing. Although conceptual, we target [http://pubs.acs.org/doi/pdfplus/10.1021/ja906987s DNA Strand Displacement] as our experimental chassis.  
+  <br>  
{ align="center"  { align="center"  
−   [[Image:  +   
−    +  [[Image:molecularreactionsarerules.gifcenterthumb300pxMolecular reactions define ''rules'' according to which reactants form products. Here molecules of type A combine with molecules of type B to form molecules of type C, at a rate proportional to the molecular concentrations of A and B as well as a rate constant ''k''.]] 
−   [[Image:  +   
−  +   
+    
+  [[Image:branchmigration.pngcenterthumb300pxWe map abstract molecular reactions to DNA reactions. Through a process  
+  called [http://pubs.acs.org/doi/pdfplus/10.1021/ja906987s DNA strand displacement], single strands of DNA displace parts of double strands, releasing other single strands.]]  
}  }  
−  We have developed a  +  '''Computational Constructs''' 
+  
+  We have developed a strategy for implementing digital logic with molecular reactions. Based on a bistable mechanism for representing bits, we implement a constituent set of logical components, including combinational components such as '''AND''', '''OR''', and '''XOR gates''', as well as sequential components such as '''D latches''' and '''D flipflops'''. Using these components, we build fullfledged digital circuits such as a ''binary counters'' and ''linear feedback shift registers''.  
{  {  
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{ style="background:#F0E68C"  { style="background:#F0E68C"  
 valign="top"   valign="top"  
−    +   width="100"  '''title''': 
−    +   width="500"  [[Media:Jiang_Riedel_Parhi_Digital_Logic_with_Molecular_Reactions.pdf  Digital Logic with Molecular Reactions]] 
−   valign="top"  +   valign="top" 
 '''authors''':   '''authors''':  
−   [[  +   [[Hua Jiang]], [[Marc Riedel]], [http://www.ece.umn.edu/users/parhi Keshab Parhi] 
−  
−  
−  
 valign="top"   valign="top"  
 '''presented at''':   '''presented at''':  
−   [http://www.  +   [http://www.iccad.com The International Conference on ComputerAided Design], San Jose, CA, 2013. 
}  }  
−   align=center width="70"   +   align="center" width="70"  
−  <span class="plainlinks">  +  <span class="plainlinks">[http://cctbio.ece.umn.edu/wiki/images/c/cf/Jiang_Riedel_Parhi_Digital_Logic_with_Molecular_Reactions.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> 
−  [http://  +  <br>[[Media:Jiang_Riedel_Parhi_Digital_Logic_with_Molecular_Reactions.pdf  Paper]] 
−  <br>  
−  [[Media:  
−  
−  
−  
}  }  
−  +  We have developed a strategy for implementing arithmetic with molecular reactions – operations such as '''increments & decrements''', '''multiplication''', '''logarithms''', and '''exponentiation'''. Try out our [http://mriedel.ece.umn.edu/chemcompiler/chemcompiler.pl compiler]: it translates arbitrary constructs from a '''Clike language''' into a robust implementation with molecular reactions.  
−  +  {  
−  +    
+  { style="background:#F0E68C"  
+   valign="top"  
+   width="100"  '''title''':  
+   width="500"  [[Media:Senum_Riedel_RateIndependent_Constructs_for_Chemical_Computation.pdf  RateIndependent Constructs for Chemical Computation]]  
+   valign="top"  
+   '''authors''':  
+   [[Phil Senum]] and [[Marc Riedel]]  
+   valign="top"  
+   '''appeared in''':  
+   [http://dx.plos.org/10.1371/journal.pone.0021414 PLoS ONE], Vol. 6, No. 6, 2011.<br>[[Rate_Independent_Constructs_Supplementary_Information  Supplementary Information]]  
+  }  
+   align="center" width="70"   
+  <span class="plainlinks">  
+  [http://mriedel.ece.umn.edu/wiki/images/d/db/Senum_Riedel_RateIndependent_Constructs_for_Chemical_Computation.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span>  
+  <br> [http://mriedel.ece.umn.edu/wiki/images/d/db/Senum_Riedel_RateIndependent_Constructs_for_Chemical_Computation.pdf Paper]  
+   align="center" width="70"   
+  <span class="plainlinks">[http://mriedel.ece.umn.edu/wiki/images/d/d2/Senum_Riedel_RateIndependent_Modules_for_Chemical_Computation.pptx http://mriedel.ece.umn.edu/wiki/images/3/36/Ppt.jpg]</span>  
+  <br> [http://mriedel.ece.umn.edu/wiki/images/d/d2/Senum_Riedel_RateIndependent_Modules_for_Chemical_Computation.pptx Slides]  
+  }  
−  +  We have developed a strategy for implementing signal processing with molecular reactions including operations such as '''filtering'''. We have demonstrated robust designs for [http://en.wikipedia.org/wiki/Finite_impulse_response FiniteImpulse Response (FIR)], [http://en.wikipedia.org/wiki/Infinite_impulse_response InfiniteImpulse Response (IIR)] filters, and [http://en.wikipedia.org/wiki/Fast_Fourier_transform Fast Fourier Transforms (FFTs)].  
{  {  
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 valign="top"   valign="top"  
 width="100"  '''title''':   width="100"  '''title''':  
−   width="500"  [[Media:  +   width="500"  [[Media:Jiang_Salehi_Riedel_Parhi_DiscreteTime_Signal_Processing_with_DNA.pdf  DiscreteTime Signal Processing with DNA]] 
 valign="top"   valign="top"  
 '''authors''':   '''authors''':  
−   [[  +   [[Hua Jiang]], Ahmed Salehi, [[Marc Riedel]] and [http://www.ece.umn.edu/users/parhi Keshab Parhi] 
+   valign="top"  
+   '''appeared in''':  
+   [http://pubs.acs.org/doi/abs/10.1021/sb300087n ACS Synthetic Biology], Vol. 2 no. 5, pp. 245–254, 2013.<br>[[Media:Jiang_Salehi_Riedel_Parhi_DiscreteTime_Signal_Processing_with_DNA_Appendix.pdf  Supplementary Information: List of Reactions]]  
+   valign="top"  
+   '''appeared in''':  
+   [http://www.computer.org/portal/web/dt IEEE Design & Test of Computers], Vol. 29, No. 3, pp. 21–31, 2012.  
 valign="top"   valign="top"  
−   '''  +   '''presented at''': 
−   [http://  +   [http://www.iccad.com/ IEEE/ACM International Conference on ComputerAided Design],<br> San Jose, CA, 2010. 
 valign="top"   valign="top"  
−   '''presented  +   '''presented at''': 
−   [http://www.  +   [http://www.wikicfp.com/cfp/servlet/event.showcfp?eventid=7703©ownerid=8242 IEEE Workshop on Signal Processing Systems], San Francisco, 2010 
}  }  
−   align=center width="70"   +   align="center" width="70"  
+  <span class="plainlinks">  
+  [http://mriedel.ece.umn.edu/wiki/images/3/36/Jiang_Salehi_Riedel_Parhi_DiscreteTime_Signal_Processing_with_DNA.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span>  
+  <br> [http://mriedel.ece.umn.edu/wiki/images/3/36/Jiang_Salehi_Riedel_Parhi_DiscreteTime_Signal_Processing_with_DNA.pdf Paper]  
+   align="center" width="70"   
<span class="plainlinks">  <span class="plainlinks">  
−  [http://  +  [http://mriedel.ece.umn.edu/wiki/images/2/2a/Jiang_Kharam_Riedel_Parhi_Digital_Signal_Processing_with_Biomolecular_Reactions.pptx http://mriedel.ece.umn.edu/wiki/images/3/36/Ppt.jpg]</span> 
+  <br> [http://mriedel.ece.umn.edu/wiki/images/2/2a/Jiang_Kharam_Riedel_Parhi_Digital_Signal_Processing_with_Biomolecular_Reactions.pptx Slides]  
+  }  
+  
<br>  <br>  
−  +  { align="center"  
−   align=center  +  
−  +    
−  +  [[Image:dnalogicgates.gifcenterthumb450px Simulations of DNA implementation of logic gates. The input signals are molecular concentrations X and Y; the output signal is a molecular concentration Z. (A) AND gate. (B) OR gate. (C) NOR gate. (D) XOR gate.]]  
+    
+   
+    
+  [[Image:movingaveragefiltersimulation.gifcenterthumb400pxSimulations of DNA implementation of a '''movingaverage FIR filter'''. This filter removes the highfrequency component from an input signal, producing an output signal consisting of only the lowfrequency component. Here the "signals" are molecular concentrations.]]  
+    
}  }  
−  Please see our "[[Papers,_Theses,  +  The impetus for this research is not computation ''per se''. Molecular computation will never compete with conventional computers made of [http://en.wikipedia.org/wiki/Integrated_circuit silicon integrated circuits] for tasks such as number crunching. Chemical systems are inherently slow and messy, taking minutes or even hours to finish, and producing fragmented results. Rather, the goal is to create “'''embedded controllers'''” – viruses and bacteria that are engineered to perform useful molecular computation ''in situ'' where it is needed, for instance for drug delivery and biochemical sensing. 
+  [[Image:embeddedcontroller.pngcenterthumb350pxMolecular computation is applicable to the design of ''embedded controllers'': engineered bacteria and viruses for tasks such as drug delivery.]]  
+  
+  Please see our "[[Papers,_Theses,_and_Presentations Publications]]" page for more of our papers on these topics.  
==Computing with Nanoscale Lattices==  ==Computing with Nanoscale Lattices==  
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In his seminal Master's Thesis, [http://en.wikipedia.org/wiki/Claude_Shannon Claude Shannon] made the connection between Boolean algebra and switching circuits. He considered '''twoterminal''' switches corresponding to electromagnetic relays. A Boolean function can be implemented in terms of connectivity across a network of switches, often arranged in a series/parallel configuration. We have developed a method for synthesizing Boolean functions with networks of '''fourterminal switches'''. Our model is applicable for variety of nanoscale technologies, such as [http://www.sciencemag.org/content/302/5649/1377.short nanowire crossbar arrays], as [http://en.wikipedia.org/wiki/Molecular_switch molecular switchbased structures].  In his seminal Master's Thesis, [http://en.wikipedia.org/wiki/Claude_Shannon Claude Shannon] made the connection between Boolean algebra and switching circuits. He considered '''twoterminal''' switches corresponding to electromagnetic relays. A Boolean function can be implemented in terms of connectivity across a network of switches, often arranged in a series/parallel configuration. We have developed a method for synthesizing Boolean functions with networks of '''fourterminal switches'''. Our model is applicable for variety of nanoscale technologies, such as [http://www.sciencemag.org/content/302/5649/1377.short nanowire crossbar arrays], as [http://en.wikipedia.org/wiki/Molecular_switch molecular switchbased structures].  
−  {align="center"  +  { align="center" 
    
[[Image:twoterminal.gifcenterthumbnone315pxShannon's model: '''twoterminal switches'''. Each switch is either ON (closed) or OFF (open). A Boolean function is implemented in terms of connectivity across a network of switches, between the source S and the drain D.]]  [[Image:twoterminal.gifcenterthumbnone315pxShannon's model: '''twoterminal switches'''. Each switch is either ON (closed) or OFF (open). A Boolean function is implemented in terms of connectivity across a network of switches, between the source S and the drain D.]]  
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{ style="background:#F0E68C"  { style="background:#F0E68C"  
−   valign=top  +   valign="top" 
 width="100" '''title''':   width="100" '''title''':  
−   width="500"[[Media:Altun_Riedel_Logic_Synthesis_for_Switching_Lattices.pdf  Logic Synthesis for Switching Lattices]]  +   width="500" [[Media:Altun_Riedel_Logic_Synthesis_for_Switching_Lattices.pdf  Logic Synthesis for Switching Lattices]] 
 valign="top"   valign="top"  
 '''authors''':   '''authors''':  
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 [http://www.dac.com/47th/index.aspx Design Automation Conference], Anaheim, CA, 2010.   [http://www.dac.com/47th/index.aspx Design Automation Conference], Anaheim, CA, 2010.  
}  }  
−   align=center width="70"   +   align="center" width="70"  
<span class="plainlinks">  <span class="plainlinks">  
−  [http://cadbio.com/wiki/images/c/ca/Altun_Riedel_Logic_Synthesis_for_Switching_Lattices.pdf  +  [http://cadbio.com/wiki/images/c/ca/Altun_Riedel_Logic_Synthesis_for_Switching_Lattices.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> 
<br>  <br>  
[[Media:Altun_Riedel_Logic_Synthesis_for_Switching_Lattices.pdf  Paper]]  [[Media:Altun_Riedel_Logic_Synthesis_for_Switching_Lattices.pdf  Paper]]  
 align="center" width="70"    align="center" width="70"   
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−  [http://mriedel.ece.umn.edu/wiki/images/2/28/Altun_Riedel_LatticeBased_Computation_of_Boolean_Functions.ppt http://  +  [http://mriedel.ece.umn.edu/wiki/images/2/28/Altun_Riedel_LatticeBased_Computation_of_Boolean_Functions.ppt http://mriedel.ece.umn.edu/wiki/images/3/36/Ppt.jpg]</span> 
<br> [http://mriedel.ece.umn.edu/wiki/images/2/28/Altun_Riedel_LatticeBased_Computation_of_Boolean_Functions.ppt Slides]  <br> [http://mriedel.ece.umn.edu/wiki/images/2/28/Altun_Riedel_LatticeBased_Computation_of_Boolean_Functions.ppt Slides]  
}  }  
The impetus for nanowirebased technology is the potential density, scalability and manufacturability. Many other novel and emerging technologies fit the general model of fourterminal switches. For instance, researchers are investigating [http://en.wikipedia.org/wiki/Spin_wave spin waves]. A common feature of many emerging technologies for switching networks is that they exhibit high defect rates.  The impetus for nanowirebased technology is the potential density, scalability and manufacturability. Many other novel and emerging technologies fit the general model of fourterminal switches. For instance, researchers are investigating [http://en.wikipedia.org/wiki/Spin_wave spin waves]. A common feature of many emerging technologies for switching networks is that they exhibit high defect rates.  
−  {align="center"  +  { align="center" 
    
−  [[Image:nanocrossbar.gifcenterthumb  +  [[Image:nanocrossbar.gifcenterthumb315pxA nanowire crossbar switch. 
The connections between horizontal and vertical  The connections between horizontal and vertical  
wires are FETlike junctions. When high or low voltages are applied to input nanowires, the  wires are FETlike junctions. When high or low voltages are applied to input nanowires, the  
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−   [[Image:percolation.gifcenterthumb  +   [[Image:percolation.gifcenterthumb315px In a switching network with defects, percolation can be exploited to produce robust Boolean functionality. Unless the defect rate exceeds an error margin, with high probability no connection forms between the top and bottom plates for logical zero ("OFF"); with high probability, a connection forms for logical one ("ON").]] 
}  }  
We have devised a novel framework for digital computation with lattices of nanoscale switches with high defect rates, based on the mathematical phenomenon of [http://en.wikipedia.org/wiki/Percolation_theory percolation]. With random connectivity, percolation gives rise to a sharp nonlinearity in the probability of global connectivity as a function of the probability of local connectivity. We exploit this phenomenon to compute Boolean functions robustly in the presence of defects.  We have devised a novel framework for digital computation with lattices of nanoscale switches with high defect rates, based on the mathematical phenomenon of [http://en.wikipedia.org/wiki/Percolation_theory percolation]. With random connectivity, percolation gives rise to a sharp nonlinearity in the probability of global connectivity as a function of the probability of local connectivity. We exploit this phenomenon to compute Boolean functions robustly in the presence of defects.  
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−   width="500"[[Media:Altun_Riedel_Robust_Computation_through_Percolation_Synthesizing_Logic_with_Percolation_in_Nanoscale_Lattices.pdf  Synthesizing Logic with Percolation in Nanoscale Lattices]]  +   width="500" [[Media:Altun_Riedel_Robust_Computation_through_Percolation_Synthesizing_Logic_with_Percolation_in_Nanoscale_Lattices.pdf  Synthesizing Logic with Percolation in Nanoscale Lattices]] 
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 '''appeared in''':   '''appeared in''':  
 [http://www.igiglobal.com/Bookstore/TitleDetails.aspx?TitleId=1117&DetailsType=Description/ International Journal of Nanotechnology and Molecular Computation], <br>Vol. 3, No. 2, pp. 12–30, 2011.   [http://www.igiglobal.com/Bookstore/TitleDetails.aspx?TitleId=1117&DetailsType=Description/ International Journal of Nanotechnology and Molecular Computation], <br>Vol. 3, No. 2, pp. 12–30, 2011.  
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 '''presented at''':   '''presented at''':  
 [http://www.dac.com/46th/index.aspx Design Automation Conference], San Francisco, CA, 2009.   [http://www.dac.com/46th/index.aspx Design Automation Conference], San Francisco, CA, 2009.  
}  }  
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−  [http://cadbio.com/wiki/images/3/3b/Altun_Riedel_Robust_Computation_through_Percolation_Synthesizing_Logic_with_Percolation_in_Nanoscale_Lattices.pdf  +  [http://cadbio.com/wiki/images/3/3b/Altun_Riedel_Robust_Computation_through_Percolation_Synthesizing_Logic_with_Percolation_in_Nanoscale_Lattices.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> 
<br>  <br>  
[[Media:Altun_Riedel_Synthesizing_Logic_with_Percolation_in_Nanoscale_Lattices.pdf  Paper]]  [[Media:Altun_Riedel_Synthesizing_Logic_with_Percolation_in_Nanoscale_Lattices.pdf  Paper]]  
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−  <span class="plainlinks">[http://mriedel.ece.umn.edu/wiki/images/f/fe/Altun_Riedel_Neuhauser_Nanoscale_Digital_Computation_Through_Percolation.ppt http://  +  <span class="plainlinks">[http://mriedel.ece.umn.edu/wiki/images/f/fe/Altun_Riedel_Neuhauser_Nanoscale_Digital_Computation_Through_Percolation.ppt http://mriedel.ece.umn.edu/wiki/images/3/36/Ppt.jpg]</span> 
<br> [http://mriedel.ece.umn.edu/wiki/images/f/fe/Altun_Riedel_Neuhauser_Nanoscale_Digital_Computation_Through_Percolation.ppt Slides]  <br> [http://mriedel.ece.umn.edu/wiki/images/f/fe/Altun_Riedel_Neuhauser_Nanoscale_Digital_Computation_Through_Percolation.ppt Slides]  
}  }  
<! [[Image:Latticedefectspercolation.gifcenterthumbnone700pxIn a switching network with defects, percolation can be exploited to produce robust Boolean functionality. Unless the defect rate exceeds an error margin, with high probability, no connection forms between the top and bottom plates for logical zero ("OFF"); with high probability, a connection forms for logical one ("ON").]] >  <! [[Image:Latticedefectspercolation.gifcenterthumbnone700pxIn a switching network with defects, percolation can be exploited to produce robust Boolean functionality. Unless the defect rate exceeds an error margin, with high probability, no connection forms between the top and bottom plates for logical zero ("OFF"); with high probability, a connection forms for logical one ("ON").]] >  
−  Please see our "[[Papers,_Theses,  +  Please see our "[[Papers,_Theses,_and_Presentations Publications]]" page for more of our papers on these topics. 
==Computing with Feedback==  ==Computing with Feedback==  
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<br>  <br>  
[[Media:Riedel_Cyclic_Combinational_Circuits.pdf  PhD Dissertation]]  [[Media:Riedel_Cyclic_Combinational_Circuits.pdf  PhD Dissertation]]  
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−  <span class="plainlinks">[http://  +  <span class="plainlinks">[http://mriedel.ece.umn.edu/files/Riedel_Cyclic_Combinational_Circuits.ppt http://mriedel.ece.umn.edu/wiki/images/3/36/Ppt.jpg]</span> 
−  <br> [http://  +  <br> [http://mriedel.ece.umn.edu/files/Riedel_Cyclic_Combinational_Circuits.ppt Slides] 
}  }  
−  Please see our [[Papers,_Theses,  +  Please see our [[Papers,_Theses,_and_Presentations  Publications]] page for more of our papers on this topic. 
==Algorithms and Data Structures==  ==Algorithms and Data Structures==  
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 [http://www.iccad.com The International Conference on ComputerAided Design], San Jose, CA, 2010.   [http://www.iccad.com The International Conference on ComputerAided Design], San Jose, CA, 2010.  
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<br>[[Media:Backes_Riedel_Reduction_Of_Interpolants_For_Logic_Synthesis.pdf  Paper]]  <br>[[Media:Backes_Riedel_Reduction_Of_Interpolants_For_Logic_Synthesis.pdf  Paper]]  
−   align=center width="70"   +   align="center" width="70"  
−  <span class="plainlinks">[http://  +  <span class="plainlinks">[http://mriedel.ece.umn.edu/wiki/images/0/00/Backes_Riedel_Reduction_Of_Interpolants_For_Logic_Synthesis.ppt http://mriedel.ece.umn.edu/wiki/images/3/36/Ppt.jpg]</span> 
−  <br> [http://  +  <br> [http://mriedel.ece.umn.edu/wiki/images/0/00/Backes_Riedel_Reduction_Of_Interpolants_For_Logic_Synthesis.ppt Slides] 
}  }  
−  Please see our "[[Papers,_Theses,  +  Please see our "[[Papers,_Theses,_and_Presentations Publications]]" page for more of our papers on this topic. (Papers on SATbased circuit verification, that is, not on squids.) 
==Mathematics==  ==Mathematics==  
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 [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WDY51WP38J1&_user=10&_coverDate=04%2F30%2F2011&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1678369105&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=057c5b37ffe293c8c2fa1d00b17d26c7&searchtype=a European Journal of Combinatorics], Vol. 32, No. 3, pp. 448–463, 2011.   [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WDY51WP38J1&_user=10&_coverDate=04%2F30%2F2011&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1678369105&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=057c5b37ffe293c8c2fa1d00b17d26c7&searchtype=a European Journal of Combinatorics], Vol. 32, No. 3, pp. 448–463, 2011.  
}  }  
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−  [http://cadbio.com/wiki/images/a/ab/Qian_Riedel_Rosenberg_Uniform_Approximation_and_Bernstein_Polynomials_with_Coefficients_in_the_Unit_Interval.pdf  +  [http://cadbio.com/wiki/images/a/ab/Qian_Riedel_Rosenberg_Uniform_Approximation_and_Bernstein_Polynomials_with_Coefficients_in_the_Unit_Interval.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> 
<br>  <br>  
[[Media:Qian_Riedel_Rosenberg_Uniform_Approximation_and_Bernstein_Polynomials_with_Coefficients_in_the_Unit_Interval.pdf  Paper]]  [[Media:Qian_Riedel_Rosenberg_Uniform_Approximation_and_Bernstein_Polynomials_with_Coefficients_in_the_Unit_Interval.pdf  Paper]]  
}  }  
−  Please see our "[[Papers,_Theses,  +  Please see our "[[Papers,_Theses,_and_Presentations Publications]]" page for more of our papers on this topic. 
Latest revision as of 21:04, 20 December 2017
"You see things; and you say, 'Why?' But I dream things that never were; and I say, 'Why not?'"–– George Bernard Shaw (1856 –1950)
Our research spans different disciplines ranging from digital circuit design, to algorithms, to mathematics, to synthetic biology. It tends to be inductive (as opposed to deductive) and conceptual (as opposed to applied). A recurring theme is building systems that compute in novel or unexpected ways with new and emerging technologies. Often, the task of analyzing the way things work in a new technology is straightforward; however the task of synthesizing new computational constructs is more challenging.
Contents
Computing with Random Bit Streams
"To invent, all you need is a pile of junk and a good imagination." –– Thomas A. Edison (1847–1931)
Humans are accustomed to counting in a positional number system – decimal radix. Nearly all computer systems operate on another positional number system – binary radix. From the standpoint of representation, such positional systems are compact: given a radix b, one can represent b^{n} distinct numbers with n digits. However, from the standpoint of computation, positional systems impose a burden: for each operation such as addition or multiplication, the signal must be "decoded", with each digit weighted according to its position. The result must be "encoded" back in positional form. Any student who has designed a binary multiplier in a course on logic design can appreciate all the complexity that goes into wiring up such an operation.
Logic that Operates on Probabilities
We advocate an alternative representation: random bit streams where the signal value is encoded by the probability of obtaining a one versus a zero. This representation is much less compact than binary radix. However, complex operations can be performed with very simple logic. For instance, multiplication can be performed with a single AND gate; scaled addition can be performed with a multiplexer (MUX).
We have developed a general method for synthesizing digital circuitry that computes on such stochastic bit streams. Our method can be used to synthesize arbitrary polynomial functions. Through polynomial approximations, it can also be used to synthesize nonpolynomial functions. Because the representation is uniform, with all bits weighted equally, the resulting circuits are highly tolerant of soft errors (i.e., bit flips).


Logic that Generates Probabilities
Schemes for probabilistic computation can exploit physical sources to generate random values in the form of bit streams. Generally, each source has a fixed bias and so provides bits that have a specific probability of being one versus zero. If many different probability values are required, it can be difficult or expensive to generate all of these directly from physical sources. In this work, we demonstrate novel techniques for synthesizing combinational logic that transforms a set of source probabilities into different target probabilities.

Computing with Crappy Clocks
Clock distribution networks are a significant source of power consumption and a major design bottleneck for highperformance circuits. We have proposed a radically new approach: splitting clock domains at a very fine level, with domains consisting of only a handful of gates each. These domains are synchrnonized by "crappy clocks", generated locally with inverter rings. This is feasible if one adopts the paradigm of computing on randomized bit streams.

Please see our "Publications" page for more of our papers on these topics.
Computing with Molecules
“If I can’t create it, I don’t understand it.” –– Richard Feynman (1918–1988)
The theory of massaction kinetics underpins our understanding of biological and chemical systems. It is a simple and elegant formalism: molecular reactions define rules according to which reactants form products; each rule fires at a rate that is proportional to the quantities of the corresponding reactants that are present. Just as electronic systems implement computation in terms of voltage (energy per unit charge), we can conceive of molecular systems that compute in terms of chemical concentrations (molecules per unit volume). We are studying techniques for implementing a variety of computational constructs with molecular reactions such as logic, memory, arithmetic, and signal processing. Although conceptual, we target DNA Strand Displacement as our experimental chassis.

Computational Constructs
We have developed a strategy for implementing digital logic with molecular reactions. Based on a bistable mechanism for representing bits, we implement a constituent set of logical components, including combinational components such as AND, OR, and XOR gates, as well as sequential components such as D latches and D flipflops. Using these components, we build fullfledged digital circuits such as a binary counters and linear feedback shift registers.

We have developed a strategy for implementing arithmetic with molecular reactions – operations such as increments & decrements, multiplication, logarithms, and exponentiation. Try out our compiler: it translates arbitrary constructs from a Clike language into a robust implementation with molecular reactions.

We have developed a strategy for implementing signal processing with molecular reactions including operations such as filtering. We have demonstrated robust designs for FiniteImpulse Response (FIR), InfiniteImpulse Response (IIR) filters, and Fast Fourier Transforms (FFTs).


The impetus for this research is not computation per se. Molecular computation will never compete with conventional computers made of silicon integrated circuits for tasks such as number crunching. Chemical systems are inherently slow and messy, taking minutes or even hours to finish, and producing fragmented results. Rather, the goal is to create “embedded controllers” – viruses and bacteria that are engineered to perform useful molecular computation in situ where it is needed, for instance for drug delivery and biochemical sensing.
Please see our "Publications" page for more of our papers on these topics.
Computing with Nanoscale Lattices
"Listen to the technology; find out what it’s telling you.” –– Carver Mead (1934– )
In his seminal Master's Thesis, Claude Shannon made the connection between Boolean algebra and switching circuits. He considered twoterminal switches corresponding to electromagnetic relays. A Boolean function can be implemented in terms of connectivity across a network of switches, often arranged in a series/parallel configuration. We have developed a method for synthesizing Boolean functions with networks of fourterminal switches. Our model is applicable for variety of nanoscale technologies, such as nanowire crossbar arrays, as molecular switchbased structures.

The impetus for nanowirebased technology is the potential density, scalability and manufacturability. Many other novel and emerging technologies fit the general model of fourterminal switches. For instance, researchers are investigating spin waves. A common feature of many emerging technologies for switching networks is that they exhibit high defect rates.
We have devised a novel framework for digital computation with lattices of nanoscale switches with high defect rates, based on the mathematical phenomenon of percolation. With random connectivity, percolation gives rise to a sharp nonlinearity in the probability of global connectivity as a function of the probability of local connectivity. We exploit this phenomenon to compute Boolean functions robustly in the presence of defects.

Please see our "Publications" page for more of our papers on these topics.
Computing with Feedback
"A person with a new idea is a crank until the idea succeeds." –– Mark Twain (1835–1910)
The accepted wisdom is that combinational circuits (i.e., memoryless circuits) must have acyclic (i.e., loopfree or feedforward) topologies. And yet simple examples suggest that this need not be so. We advocate the design of cyclic combinational circuits (i.e., circuits with loops or feedback paths). We have proposed a methodology for synthesizing such circuits and demonstrated that it produces significant improvements in area and in delay.

Please see our Publications page for more of our papers on this topic.
Algorithms and Data Structures
"There are two kinds of people in the world: those who divide the world into two kinds of people, and those who don't." –– Robert Charles Benchley (1889–1945)
Consider the task of designing a digital circuit with 256 inputs. From a mathematical standpoint, such a circuit performs mappings from a space of <math>2^{256}</math> Boolean input values to Boolean output values. (The number of rows in a truth table for such a function is approximately equal to the number of atoms in the universe – <math>10^{77}</math> rows versus <math>10^{79}</math> atoms!) Verifying such a function, let alone designing the corresponding circuit, would seem to be an intractable problem. Circuit designers have succeeded in their endeavor largely as a result of innovations in the data structures and algorithms used to represent and manipulate Boolean functions. We have developed novel, efficient techniques for synthesizing functional dependencies based on socalled SATsolving algorithms. We use Craig Interpolation to generate circuits from the corresponding Boolean functions.

Please see our "Publications" page for more of our papers on this topic. (Papers on SATbased circuit verification, that is, not on squids.)
Mathematics
"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." –– Bertrand Russell (1872–1970)
The great mathematician John von Neumann articulated the view that research should never meander too far down theoretical paths; it should always be guided by potential applications. This view was not based on concerns about the relevance of his profession; rather, in his judgment, realworld applications give rise to the most interesting problems for mathematicians to tackle. At their core, most of our research contributions are mathematical contributions. The tools of our trade are discrete math, including combinatorics and probability theory.

Please see our "Publications" page for more of our papers on this topic.