There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

The organization of behavior: A neuropsychological theory

Driven by the visions of Internet of Things and 5G communications, recent years have seen a paradigm shift in mobile computing, from the centralized mobile cloud computing toward mobile edge computing (MEC). The main feature of MEC is to push mobile computing, network control and storage to the network edges (e.g., base stations and access points) so as to enable computation-intensive and latency-critical applications at the resource-limited mobile devices. MEC promises dramatic reduction in latency and mobile energy consumption, tackling the key challenges for materializing 5G vision. The promised gains of MEC have motivated extensive efforts in both academia and industry on developing the technology. A main thrust of MEC research is to seamlessly merge the two disciplines of wireless communications and mobile computing, resulting in a wide-range of new designs ranging from techniques for computation offloading to network architectures. This paper provides a comprehensive survey of the state-of-the-art MEC research with a focus on joint radio-and-computational resource management. We also discuss a set of issues, challenges, and future research directions for MEC research, including MEC system deployment, cache-enabled MEC, mobility management for MEC, green MEC, as well as privacy-aware MEC. Advancements in these directions will facilitate the transformation of MEC from theory to practice. Finally, we introduce recent standardization efforts on MEC as well as some typical MEC application scenarios.

A Survey on Mobile Edge Computing: The Communication Perspective

Towards understanding energy requirements for computation with noisy gates, we consider the computation of an arbitrary k-input, k-output binary invertible function. For broader applicability of our results, we allow using some noiseless gates in conjugation with noisy ones. However, we stipulate that the input gates on the computation graph must be separated from the output nodes by a “noisy cut.” We show that for the “information-friction” model proposed recently for energy consumed in circuits, and for binary-input AWGN noise in the computational nodes (with fixed communication schedule), the total (gate + info-friction) energy consumption for reliable computation must diverge to infinity as the target error probability is lowered to zero. Thus, in this model, the capacity of noisy computing is zero regardless of how “rate” of computation is defined: the required energy is unbounded for reliable computation regardless of how efficiently the available resources (e.g. gates, wires, etc.) are used.

Is “Shannon-capacity of noisy computing” zero?

This paper answers a question raised by Doyle on the relevance of the Witsenhausen counterexample as a toy decentralized control problem The question has two sides, the first of which focuses on the lack of an external channel in the counterexample Using existing results, we argue that the core difficulty in the counterexample is retained even in the presence of such a channel The second side questions the LQG formulation of the counterexample We consider alternative formulations and show that the understanding developed for the LQG case guides the investigation for these other cases as well Specifically, we consider 1) a variation on the original counterexample with general, but bounded, noise distributions, and 2) an adversarial extension with bounded disturbance and quadratic costs For each of these formulations, we show that quantization-based nonlinear strategies outperform linear strategies by an arbitrarily large factor Further, these nonlinear strategies also perform within a constant factor of the optimal, uniformly over all possible parameter choices (for fixed noise distributions in the Bayesian case) 
Fortuitously, the assumption of bounded noise results in a significant simplification of proofs as compared to those for the LQG formulation Therefore, the results in this paper are also of pedagogical interest

Is Witsenhausen's counterexample a relevant toy?

We argue that Witsenhausen's counterexample provides a useful conceptual bridge between distributed control, communication and computation. Inspired by the utility of studying long block-lengths in information theory, we formulate a vector version of the counterexample. Information-theoretic arguments are then used to derive bounds on the minimum cost for the vector problem. Restricted to the scalar case, the lower bounds are a strict improvement over Witsenhausen's lower bound for some parameter values. The upper bounds are based on two strategies that can asymptotically outperform optimal linear and nonlinear scalar strategies. To investigate the computational aspects of such problems, we then consider a simpler problem of lossless source coding. From a distributed control perspective, the computations required for encoding and decoding can be viewed as internal communication between virtually distributed agents. We derive new lower bounds that establish a tradeoff between the computation, communication and distortion costs for lossless source coding.

/pdf/a-vector-version-of-witsenhausen-s-counterexample-a-2g1qbzjntw.pdf

A vector version of witsenhausen’s counterexample: A convergence of control, communication and computation

We present a novel signal processing algorithm for automated, noninvasive detection of Cortical Spreading Depolarizations (CSDs) using electroencephalography (EEG) signals and validate the algorithm on simulated EEG signals. CSDs are waves of neurochemical changes that suppress neuronal activity as they propagate across the brain’s cortical surface. CSDs are believed to mediate secondary brain damage after brain trauma and cerebrovascular diseases like stroke. We address key challenges in detecting CSDs from EEG signals: (i) decay of high spatial frequencies as they travel from the cortical surface to the scalp surface; and (ii) presence of sulci and gyri, which makes it difficult to track the CSD waves as they travel across the cortex. Our algorithm detects and tracks “wavefronts” of the CSD wave, and stitches together data across space and time to decide on the presence of a CSD wave. To test our algorithm, we provide different models and complex patterns of CSD waves, including different widths of CSD suppressions, and use these models to simulate scalp EEG signals using head models of 4 subjects from the OASIS dataset. Our results suggest that the average width of suppression that a low-density EEG grid of 40 electrodes can detect is 1.1 cm, which includes a vast majority of CSD suppressions, but not all. A higher density EEG grid having 340 electrodes can detect complex CSD patterns as thin as 0.43 cm (less than minimum widths reported in prior works), among which single-gyrus propagation is the hardest to detect because of its small suppression area.

https://www.biorxiv.org/content/biorxiv/early/2018/08/16/393058.full.pdf

An algorithm for automated, noninvasive detection of cortical spreading depolarizations based on EEG simulations

We utilize single neuron models to understand mechanisms behind Temporal Interference (TI) stimulation (also called “Interferential Stimulation”). We say that a neuron exhibits TI stimulation if it does not fire for a high-frequency sinusoidal input, but fires when the input is a low-frequency modulation of the high-frequency sinusoid (specifically that generated by addition of two high frequency sinusoids with a small difference in their frequencies), while the maximum amplitude is kept the same in both cases. Our key observation – that holds for both FitzHugh-Nagumo and Hodgkin-Huxley neuron models – is that for neuron models that do exhibit TI stimulation, a high frequency pure sinusoidal input results in a current balance between inward and outward currents. This current balance leads to a subthreshold periodic orbit that keeps the membrane potential from spiking for sinusoidal inputs. However, the balance is disturbed when the envelope of the sinusoids is modulated with a high slope: the fast-changing envelope activates fast depolarizing currents without giving slow outward currents time to respond. This imbalance causes the membrane potential to build up, causing the neuron to fire. This mechanistic understanding can help design current waveforms for neurons that exhibit TI stimulation.

/pdf/the-mechanics-of-temporal-interference-stimulation-3xrjkohxyj.pdf

Pulkit Grover

Papers

Is “Shannon-capacity of noisy computing” zero?

Is Witsenhausen's counterexample a relevant toy?

A vector version of witsenhausen’s counterexample: A convergence of control, communication and computation

An algorithm for automated, noninvasive detection of cortical spreading depolarizations based on EEG simulations

The Mechanics of Temporal Interference Stimulation