Counting to Ten with Two Fingers: Compressed Counting with Spiking Neurons

We consider the task of measuring time with probabilistic threshold gates implemented by bio-inspired spiking neurons. In the model of spiking neural networks, network evolves in discrete rounds, where in each round, neurons fire in pulses in response to a sufficiently high membrane potential. This potential is induced by spikes from neighboring neurons that fired in the previous round, which can have either an excitatory or inhibitory effect. Discovering the underlying mechanisms by which the brain perceives the duration of time is one of the largest open enigma in computational neuro-science. To gain a better algorithmic understanding onto these processes, we introduce the neural timer problem. In this problem, one is given a time parameter t, an input neuron x, and an output neuron y. It is then required to design a minimum sized neural network (measured by the number of auxiliary neurons) in which every spike from x in a given round i, makes the output y fire for the subsequent t consecutive rounds. We first consider a deterministic implementation of a neural timer and show that Theta(log t) (deterministic) threshold gates are both sufficient and necessary. This raised the question of whether randomness can be leveraged to reduce the number of neurons. We answer this question in the affirmative by considering neural timers with spiking neurons where the neuron y is required to fire for t consecutive rounds with probability at least 1-delta, and should stop firing after at most 2t rounds with probability 1-delta for some input parameter delta in (0,1). Our key result is a construction of a neural timer with O(log log 1/delta) spiking neurons. Interestingly, this construction uses only one spiking neuron, while the remaining neurons can be deterministic threshold gates. We complement this construction with a matching lower bound of Omega(min{log log 1/delta, log t}) neurons. This provides the first separation between deterministic and randomized constructions in the setting of spiking neural networks. Finally, we demonstrate the usefulness of compressed counting networks for synchronizing neural networks. In the spirit of distributed synchronizers [Awerbuch-Peleg, FOCS\u2790], we provide a general transformation (or simulation) that can take any synchronized network solution and simulate it in an asynchronous setting (where edges have arbitrary response latencies) while incurring a small overhead w.r.t the number of neurons and computation time

Random Sketching, Clustering, and Short-Term Memory in Spiking Neural Networks

We study input compression in a biologically inspired model of neural computation. We demonstrate that a network consisting of a random projection step (implemented via random synaptic connectivity) followed by a sparsification step (implemented via winner-take-all competition) can reduce well-separated high-dimensional input vectors to well-separated low-dimensional vectors. By augmenting our network with a third module, we can efficiently map each input (along with any small perturbations of the input) to a unique representative neuron, solving a neural clustering problem. Both the size of our network and its processing time, i.e., the time it takes the network to compute the compressed output given a presented input, are independent of the (potentially large) dimension of the input patterns and depend only on the number of distinct inputs that the network must encode and the pairwise relative Hamming distance between these inputs. The first two steps of our construction mirror known biological networks, for example, in the fruit fly olfactory system [Caron et al., 2013; Lin et al., 2014; Dasgupta et al., 2017]. Our analysis helps provide a theoretical understanding of these networks and lay a foundation for how random compression and input memorization may be implemented in biological neural networks. Technically, a contribution in our network design is the implementation of a short-term memory. Our network can be given a desired memory time t_m as an input parameter and satisfies the following with high probability: any pattern presented several times within a time window of t_m rounds will be mapped to a single representative output neuron. However, a pattern not presented for c?t_m rounds for some constant c>1 will be "forgotten", and its representative output neuron will be released, to accommodate newly introduced patterns

The Computational Cost of Asynchronous Neural Communication

Biological neural computation is inherently asynchronous due to large variations in neuronal spike timing and transmission delays. So-far, most theoretical work on neural networks assumes the synchronous setting where neurons fire simultaneously in discrete rounds. In this work we aim at understanding the barriers of asynchronous neural computation from an algorithmic perspective. We consider an extension of the widely studied model of synchronized spiking neurons [Maass, Neural Networks 97] to the asynchronous setting by taking into account edge and node delays. - Edge Delays: We define an asynchronous model for spiking neurons in which the latency values (i.e., transmission delays) of non self-loop edges vary adversarially over time. This extends the recent work of [Hitron and Parter, ESA\u2719] in which the latency values are restricted to be fixed over time. Our first contribution is an impossibility result that implies that the assumption that self-loop edges have no delays (as assumed in Hitron and Parter) is indeed necessary. Interestingly, in real biological networks self-loop edges (a.k.a. autapse) are indeed free of delays, and the latter has been noted by neuroscientists to be crucial for network synchronization. To capture the computational challenges in this setting, we first consider the implementation of a single NOT gate. This simple function already captures the fundamental difficulties in the asynchronous setting. Our key technical results are space and time upper and lower bounds for the NOT function, our time bounds are tight. In the spirit of the distributed synchronizers [Awerbuch and Peleg, FOCS\u2790] and following [Hitron and Parter, ESA\u2719], we then provide a general synchronizer machinery. Our construction is very modular and it is based on efficient circuit implementation of threshold gates. The complexity of our scheme is measured by the overhead in the number of neurons and the computation time, both are shown to be polynomial in the largest latency value, and the largest incoming degree ? of the original network. - Node Delays: We introduce the study of asynchronous communication due to variations in the response rates of the neurons in the network. In real brain networks, the round duration varies between different neurons in the network. Our key result is a simulation methodology that allows one to transform the above mentioned synchronized solution under edge delays into a synchronized under node delays while incurring a small overhead w.r.t space and time

Lendo Celan no Brasil: a recepção de Celan em "Logocausto", de Leandro Sarmatz

Este artigo aborda a recepção de Paulo Celan no cenário poético brasileiro contemporâneo, tomando como exemplo a poética típica de Celan presente em Logocausto (2009), de Leandro Sarmatz. Sugiro que os dois poetas compartilham de uma preocupação profunda com a destruição do judaísmo europeu, que moldou suas respectivas poéticas de maneira semelhante. Minha análise investigará o motivo poético de presentear e retratará o processo de recepção como um modo de aceitação ou de recusa do presente, neste caso, tratando-se de um corpus linguístico. Em termos históricos, a recepção de Paul Celan em português deve ser analisada em termos de posicionamento da voz poética: enquanto Celan constrói uma poética da extinção a partir da perspectiva do testemunho – isto é, a partir da linguagem do evento – Sarmatz a descreve a partir da perspectiva de um observador envolvido, porém estranho, um tradutor

Joint Unitary Triangularization for Gaussian Multi-User MIMO Networks

The problem of transmitting a common message to multiple users over the Gaussian multiple-input multiple-output broadcast channel is considered, where each user is equipped with an arbitrary number of antennas. A closed-loop scenario is assumed, for which a practical capacity-approaching scheme is developed. By applying judiciously chosen unitary operations at the transmit and receive nodes, the channel matrices are triangularized so that the resulting matrices have equal diagonals, up to a possible multiplicative scalar factor. This, along with the utilization of successive interference cancellation, reduces the coding and decoding tasks to those of coding and decoding over the single-antenna additive white Gaussian noise channel. Over the resulting effective channel, any off-the-shelf code may be used. For the two-user case, it was recently shown that such joint unitary triangularization is always possible. In this paper, it is shown that for more than two users, it is necessary to carry out the unitary linear processing jointly over multiple channel uses, i.e., space-time processing is employed. It is further shown that exact triangularization, where all resulting diagonals are equal, is still not always possible, and appropriate conditions for the existence of such are established for certain cases. When exact triangularization is not possible, an asymptotic construction is proposed, that achieves the desired property of equal diagonals up to edge effects that can be made arbitrarily small, at the price of processing a sufficiently large number of channel uses together.Comment: Extended version of published paper in IEEE Transactions on Information Theory, vol. 61, no. 5, pp. 2662-2692, May 201

AN OPTIMIZED SOLID-PHASE REDUCTION AND CAPTURE STRATEGY FOR THE STUDY OF REVERSIBLY-OXIDIZED CYSTEINES AND ITS APPLICATION TO METAL TOXICITY

The reversible oxidation of cysteine by reactive oxygen species (ROS) is both a mechanism for cellular protein signaling as well as a cause of cellular injury and death through the generation of oxidative stress. The study of cysteine oxidation is complicated by the methodology currently available to isolate and enrich oxidized-cysteine containing proteins. We sought to simplify this process by reducing the time needed to process samples and reducing sample loss and contamination risk. We accomplished this by eliminating precipitation steps needed for the protocol by (a) introducing an in-solution NEM-quenching step prior to reduction and (b) replacing soluble dithiothreitol reductant with a series of newly-developed high-capacity polyacrylamide-based solid-phase reductants that could be easily separated from the lysate through centrifugation. These modifications, collectively called resin-assisted reduction and capture (RARC), reduced the time needed to perform the RAC method from 2-3 days to 4-5 hours, while the overall quality and quantity of previously-oxidized cysteines captured was increased. In order to demonstrate the RARC method’s utility in studying complex cellular oxidants, the optimized methodology was used to study cysteine oxidation caused by the redox-active metals arsenic, cadmium, and chromium. As(III), Cr(VI), and Cd(II) were all found to increase cysteine oxidation significantly, with As(III) and Cd(II) inducing more oxidation than Cr(VI) following a 24-hour exposure to cytotoxic concentrations. Label-free proteomic analysis and western blotting of RARC-isolated oxidized proteins found a high degree of commonality between the proteins oxidized by these metals, with cytoskeletal, translational, stress response, and metabolic proteins all being oxidized. Several previously-unreported redox-active cysteines were also identified. These results indicate that cysteine oxidation by As(III), Cr(VI), and Cd(II) may play a significant role in these metals’ cytotoxicity and demonstrates the utility of the RARC method as a strategy for studying reversible cysteine oxidation by oxidants in oxidative signaling and disease. The RARC method is a simplification and improvement upon the current state of the art which decreases the barrier of entry to studying cysteine oxidation, allowing more researchers to study this modification. We predict that the RARC methodology will be critical in expanding our understanding of reactive cysteines in cellular function and disease

THE INFLUENCE OF ANTIDIABETIC MEDICATIONS ON THE DEVELOPMENT AND PROGRESSION OF PROSTATE CANCER

The development of prostate tumors has been linked to co-morbid diabetes mellitus (DM) in several studies, potentially through the stimulation of insulin-like growth factor receptor (IGFR). This study evaluates the effect of anti-diabetic medication use on the development of high grade tumors and time to tumor progression compared to non-diabetics. This retrospective, nested case control study identified patients with prostate cancer (PCa) from the Kentucky Medicaid Database. Cases were diagnosed with PCa and DM and using at least one of the following antidiabetic medications; sulfonylureas, insulin, metformin or TZDs. Cases were further stratified on their insulin exposure resulting from therapy. Controls were those with PCa without DM or any anti-diabetic medications. No statistically significant effects on insulin exposure was found on tumor grade and time to progression. Trends identified that use of metformin or TZDs potentially decreased the odds of high-grade tumors and decreased the risk of progression, while sulfonylureas and high-dose insulin may increase the odds of high-grade tumors and increase the risk of progression compared to non-diabetics. Future studies should be conducted to further evaluate the effects of anti-diabetic medications on tumor grade and time to prostate cancer progression

Broadcast CONGEST Algorithms against Adversarial Edges

We consider the corner-stone broadcast task with an adaptive adversary that controls a fixed number of $t$ edges in the input communication graph. In this model, the adversary sees the entire communication in the network and the random coins of the nodes, while maliciously manipulating the messages sent through a set of $t$ edges (unknown to the nodes). Since the influential work of [Pease, Shostak and Lamport, JACM'80], broadcast algorithms against plentiful adversarial models have been studied in both theory and practice for over more than four decades. Despite this extensive research, there is no round efficient broadcast algorithm for general graphs in the CONGEST model of distributed computing. We provide the first round-efficient broadcast algorithms against adaptive edge adversaries. Our two key results for $n$-node graphs of diameter $D$ are as follows: 1. For $t=1$, there is a deterministic algorithm that solves the problem within $\widetilde{O}(D^2)$ rounds, provided that the graph is 3 edge-connected. This round complexity beats the natural barrier of $O(D^3)$ rounds, the existential lower bound on the maximal length of $3$ edge-disjoint paths between a given pair of nodes in $G$. This algorithm can be extended to a $\widetilde{O}(D^{O(t)})$-round algorithm against $t$ adversarial edges in $(2t+1)$ edge-connected graphs. 2. For expander graphs with minimum degree of $\Omega(t^2\log n)$, there is an improved broadcast algorithm with $O(t \log ^2 n)$ rounds against $t$ adversarial edges. This algorithm exploits the connectivity and conductance properties of G-subgraphs obtained by employing the Karger's edge sampling technique. Our algorithms mark a new connection between the areas of fault-tolerant network design and reliable distributed communication.Comment: accepted to DISC2