Faithful Encoding Research Articles

A Noise-Tolerant Differentiable Learning Approach for Single Occurrence Regular Expression with Interleaving

We study the problem of learning a single occurrence regular expression with interleaving (SOIRE) from a set of text strings possibly with noise. SOIRE fully supports interleaving and covers a large portion of regular expressions used in practice. Learning SOIREs is challenging because it requires heavy computation and text strings usually contain noise in practice. Most of the previous studies only learn restricted SOIREs and are not robust on noisy data. To tackle these issues, we propose a noise-tolerant differentiable learning approach SOIREDL for SOIRE. We design a neural network to simulate SOIRE matching and theoretically prove that certain assignments of the set of parameters learnt by the neural network, called faithful encodings, are one-to-one corresponding to SOIREs for a bounded size. Based on this correspondence, we interpret the target SOIRE from an assignment of the set of parameters of the neural network by exploring the nearest faithful encodings. Experimental results show that SOIREDL outperforms the state-of-the-art approaches, especially on noisy data.

Rewriting theory for the life sciences: A unifying theory of CTMC semantics

The Kappa biochemistry and the MØD organic chemistry frameworks are amongst the most intensely developed applications of rewriting-based methods in the life sciences to date. A typical feature of these types of rewriting theories is the necessity to implement certain structural constraints on the objects to be rewritten (a protein is empirically found to have a certain signature of sites, a carbon atom can form at most four bonds, ...). In this paper, we contribute a number of original developments that permit to implement a universal theory of continuous-time Markov chains (CTMCs) for stochastic rewriting systems. Our core mathematical concepts are a novel rule algebra construction for the relevant setting of rewriting rules with conditions, both in Double- and in Sesqui-Pushout semantics, augmented by a suitable stochastic mechanics formalism extension that permits to derive dynamical evolution equations for pattern-counting statistics. A second main contribution of our paper is a novel framework of restricted rewriting theories, which comprises a rule-algebra calculus under the restriction to so-called constraint-preserving completions of application conditions (for rules considered to act only upon objects of the underlying category satisfying a globally fixed set of structural constraints). This novel framework in turn renders a faithful encoding of bio- and organo-chemical rewriting in the sense of Kappa and MØD possible, which allows us to derive a rewriting-based formulation of reaction systems including a full-fledged CTMC semantics as instances of our universal CTMC framework. While offering an interesting new perspective and conceptual simplification of this semantics in the setting of Kappa, both the formal encoding and the CTMC semantics of organo-chemical reaction systems as motivated by the MØD framework are the first such results of their kind.

Neural variability determines coding strategies for natural self-motion in macaque monkeys.

We have previously reported that central neurons mediating vestibulo-spinal reflexes and self-motion perception optimally encode natural self-motion (Mitchell et al., 2018). Importantly however, the vestibular nuclei also comprise other neuronal classes that mediate essential functions such as the vestibulo-ocular reflex (VOR) and its adaptation. Here we show that heterogeneities in resting discharge variability mediate a trade-off between faithful encoding and optimal coding via temporal whitening. Specifically, neurons displaying lower variability did not whiten naturalistic self-motion but instead faithfully represented the stimulus' detailed time course, while neurons displaying higher variability displayed temporal whitening. Using a well-established model of VOR pathways, we demonstrate that faithful stimulus encoding is necessary to generate the compensatory eye movements found experimentally during naturalistic self-motion. Our findings suggest a novel functional role for variability toward establishing different coding strategies: (1) faithful stimulus encoding for generating the VOR; (2) optimized coding via temporal whitening for other vestibular functions.

Two sides of the same coin: session types and game semantics: a synchronous side and an asynchronous side

Game semantics and session types are two formalisations of the same concept: message-passing open programs following certain protocols. Game semantics represents protocols as games, and programs as strategies; while session types specify protocols, and well-typed π-calculus processes model programs. Giving faithful models of the π-calculus and giving a precise description of strategies as a programming language are two difficult problems. In this paper, we show how these two problems can be tackled at the same time by building an accurate game semantics model of the session π-calculus. Our main contribution is to fill a semantic gap between the synchrony of the (session) π-calculus and the asynchrony of game semantics, by developing an event-structure based game semantics for synchronous concurrent computation. This model supports the first truly concurrent fully abstract (for barbed congruence) interpretation of the synchronous (session) π-calculus. We further strengthen this correspondence, establishing finite definability of asynchronous strategies by the internal session π-calculus. As an application of these results, we propose a faithful encoding of synchronous strategies into asynchronous strategies by call-return protocols, which induces automatically an encoding at the level of processes. Our results bring session types and game semantics into the same picture, proposing the session calculus as a programming language for strategies, and strategies as a very accurate model of the session calculus. We implement a prototype which computes the interpretation of session processes as synchronous strategies.

Faithful (meta-)encodings of programmable strategies into term rewriting systems

We consider the problem of inferring a grammar describing the output of a functional program given a grammar describing its input. Solutions to this problem are helpful for detecting bugs or proving safety properties of functional programs, and several rewriting tools exist for solving this problem. However, known grammar inference techniques are not able to take evaluation strategies of the program into account. This yields very imprecise results when the evaluation strategy matters. In this work, we adapt the Tree Automata Completion algorithm to approximate accurately the set of terms reachable by rewriting under the innermost strategy. We formally prove that the proposed technique is sound and precise w.r.t. innermost rewriting. We show that those results can be extended to the leftmost and rightmost innermost case. The algorithms for the general innermost case have been implemented in the Timbuk reachability tool. Experiments show that it noticeably improves the accuracy of static analysis for functional programs using the call-by-value evaluation strategy.

Development of a combined magnetic encoder

Purpose As a type of angular displacement sensor, the Hall-effect magnetic encoder incorporates many advantages. While compared with the photoelectric encoder, the magnetic encoder nevertheless has lower precision and lower resolution. So, the purpose of this essay is to find a way to increase the precision and resolution of the magnetic encoder. Design/methodology/approach By combining a single-pole magnetic encoder and a multi-pole AlNiCo magnet, the precision and resolution of this combined magnetic encoder are increased without increasing its volume or complicating its structure. A special algorithm system is developed to ensure faithful encoding and decoding. Findings Tests show that the combined magnetic encoder, with a diameter of 67.12 mm (including shaft) and thickness of 6.9 mm, has a precision of ±6′, compared with a 15-bit photoelectric encoder and a static resolution of ±0.6′. Originality/value This new kind of magnetic encoder could be used in specialized fields which need high-precision servo-control systems that are small, have ultra-low-speed and high-speed ratios and are non-oil-polluting or shock-resistant.

Encoding the Factorisation Calculus

Jay and Given-Wilson have recently introduced the Factorisation (or SF-) calculus as a minimal fundamental model of intensional computation. It is a combinatory calculus containing a special combinator, F, which is able to examine the internal structure of its first argument. The calculus is significant in that as well as being combinatorially complete it also exhibits the property of structural completeness, i.e. it is able to represent any function on terms definable using pattern matching on arbitrary normal forms. In particular, it admits a term that can decide the structural equality of any two arbitrary normal forms. Since SF-calculus is combinatorially complete, it is clearly at least as powerful as the more familiar and paradigmatic Turing-powerful computational models of Lambda Calculus and Combinatory Logic. Its relationship to these models in the converse direction is less obvious, however. Jay and Given-Wilson have suggested that SF-calculus is strictly more powerful than the aforementioned models, but a detailed study of the connections between these models is yet to be undertaken. This paper begins to bridge that gap by presenting a faithful encoding of the Factorisation Calculus into the Lambda Calculus preserving both reduction and strong normalisation. The existence of such an encoding is a new result. It also suggests that there is, in some sense, an equivalence between the former model and the latter. We discuss to what extent our result constitutes an equivalence by considering it in the context of some previously defined frameworks for comparing computational power and expressiveness.

Structure and function of a complex sensory synapse

Vision is the most important of the senses for humans, and the retina is the first stage in the processing of light signals in the visual system. In the retina, highly specialized light-sensing neurons, the rod and cone photoreceptors, convert light into neural signals. These signals are extensively processed and filtered in the subsequent retinal network before transmitted to the higher visual centres in the brain, where the perception of viewed objects and scenes is finally constructed. A key feature of signal processing in the mammalian retina is parallel processing. Visual information is segregated in parallel pathways already at the rod and cone photoreceptor terminals, which provide multiple output synapses for the faithful encoding and transfer of the visual signals to the post-receptoral retinal network. This review aims at highlighting the current knowledge about the structural and functional pre- and post-synaptic specializations of rod and cone photoreceptor ribbon synapses, which belong to the most complex chemical synapses in the central nervous system.

In vivo conditions induce faithful encoding of stimuli by reducing nonlinear synchronization in vestibular sensory neurons.

Previous studies have shown that neurons within the vestibular nuclei (VN) can faithfully encode the time course of sensory input through changes in firing rate in vivo. However, studies performed in vitro have shown that these same VN neurons often display nonlinear synchronization (i.e. phase locking) in their spiking activity to the local maxima of sensory input, thereby severely limiting their capacity for faithful encoding of said input through changes in firing rate. We investigated this apparent discrepancy by studying the effects of in vivo conditions on VN neuron activity in vitro using a simple, physiologically based, model of cellular dynamics. We found that membrane potential oscillations were evoked both in response to step and zap current injection for a wide range of channel conductance values. These oscillations gave rise to a resonance in the spiking activity that causes synchronization to sinusoidal current injection at frequencies below 25 Hz. We hypothesized that the apparent discrepancy between VN response dynamics measured in in vitro conditions (i.e., consistent with our modeling results) and the dynamics measured in vivo conditions could be explained by an increase in trial-to-trial variability under in vivo vs. in vitro conditions. Accordingly, we mimicked more physiologically realistic conditions in our model by introducing a noise current to match the levels of resting discharge variability seen in vivo as quantified by the coefficient of variation (CV). While low noise intensities corresponding to CV values in the range 0.04–0.24 only eliminated synchronization for low (<8 Hz) frequency stimulation but not high (>12 Hz) frequency stimulation, higher noise intensities corresponding to CV values in the range 0.5–0.7 almost completely eliminated synchronization for all frequencies. Our results thus predict that, under natural (i.e. in vivo) conditions, the vestibular system uses increased variability to promote fidelity of encoding by single neurons. This prediction can be tested experimentally in vitro.

Musical experience shapes human brainstem encoding of linguistic pitch patterns.

Music and speech are very cognitively demanding auditory phenomena generally attributed to cortical rather than subcortical circuitry. We examined brainstem encoding of linguistic pitch and found that musicians show more robust and faithful encoding compared with nonmusicians. These results not only implicate a common subcortical manifestation for two presumed cortical functions, but also a possible reciprocity of corticofugal speech and music tuning, providing neurophysiological explanations for musicians' higher language-learning ability.

On the representation of McCarthy's [formula omitted] in the [formula omitted]-calculus

We study the encoding of λ [ ] , the call-by-name λ -calculus enriched with McCarthy's amb operator, into the π -calculus. Semantically, amb is a challenging operator, for the fairness constraints that it expresses. We prove that, under a certain interpretation of divergence in the λ -calculus ( weak divergence), a faithful encoding is impossible. However, with a different interpretation of divergence ( strong divergence), the encoding is possible, and for this case we derive results and coinductive proof methods to reason about λ [ ] that are similar to those for the encoding of pure λ -calculi. We then use these methods to derive the most important laws concerning amb. We take bisimilarity as behavioural equivalence on the π -calculus, which sheds some light on the relationship between fairness and bisimilarity.

On the Representation of McCarthy's amb in the π-calculus

We study the encoding of ▪, the call by name λ-calculus enriched with McCarthy's amb operator, into the π-calculus. Semantically, amb is a challenging operator, for the fairness constraints that it expresses. We prove that, under a certain interpretation of divergence in the λ-calculus (weak divergence), a faithful encoding is impossible. However, with a different interpretation of divergence (strong divergence), the encoding is possible, and for this case we derive results and coinductive proof methods to reason about ▪ that are similar to those for the encoding of pure λ-calculi. We then use these methods to derive the most important laws concerning amb. We take bisimilarity as behavioural equivalence on the π-calculus, which sheds some light on the relationship between fairness and bisimilarity. As a spin-off result, we show that there is no small-step operational semantics for ▪ that preserves the branching structure of terms and yields the correct predicates of convergence and (weak) divergence

Variability and coding efficiency of noisy neural spike encoders

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders — an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal membrane containing stochastic Na + and K + channels obeying Hodgkin–Huxley kinetics. The quality of signal encoding is assessed by reconstructing the input stimuli from the output spike trains using optimal linear mean square estimation. A comparison of the estimation performance of noisy neuronal models of spike generation enables us to assess the impact of neuronal noise on the efficacy of neural coding. The results for both models suggest that spike timing variability reduces the ability of spike trains to encode rapid time-varying stimuli. Moreover, contrary to expectations based on earlier studies, we find that the noisy spike encoding models encode slowly varying stimuli more effectively than rapidly varying ones.

Bayesian conditioning in possibility theory

In this paper, possibility measures are viewed as upper bounds of ill-known probabilities, since a possibility distribution is a faithful encoding of a set of lower bounds of probabilities bearing on a nested collection of subsets. Two kinds of conditioning can be envisaged in this framework, namely revision and focusing. On the one hand, revision by a sure event corresponds to adding an extra constraint enforcing that this event is impossible. On the other hand, focusing amounts to a sensitivity analysis on the conditioned probability measures (induced by the lower bound constraints). When focusing on a particular situation, the generic knowledge encoded by the probability bounds is applied to this situation, without aiming at modifying the generic knowledge. It contrasts with revision where the generic knowledge is modified by the new constraint. This paper proves that focusing applied to a possibility measure yields a possibility measure again, which means that the conditioning of a family of probabilities, induced by lower bounds bearing on probabilities of nested events, can be faithfully handled on the possibility representation itself. Relationships with similar results in the belief function setting are pointed out. Lastly the application of possibilistic focusing to exception-tolerant inference is suggested.