A Low Density Lattice Decoder via Non-Parametric Belief Propagation

The recent work of Sommer, Feder and Shalvi presented a new family of codes called low density lattice codes (LDLC) that can be decoded efficiently and approach the capacity of the AWGN channel. A linear time iterative decoding scheme which is based on a message-passing formulation on a factor graph is given. In the current work we report our theoretical findings regarding the relation between the LDLC decoder and belief propagation. We show that the LDLC decoder is an instance of non-parametric belief propagation and further connect it to the Gaussian belief propagation algorithm. Our new results enable borrowing knowledge from the non-parametric and Gaussian belief propagation domains into the LDLC domain. Specifically, we give more general convergence conditions for convergence of the LDLC decoder (under the same assumptions of the original LDLC convergence analysis). We discuss how to extend the LDLC decoder from Latin square to full rank, non-square matrices. We propose an efficient construction of sparse generator matrix and its matching decoder. We report preliminary experimental results which show our decoder has comparable symbol to error rate compared to the original LDLC decoder.%Comment: Submitted for publicatio

Well structured program equivalence is highly undecidable

We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the construction of program equivalence, which returns the value $\mathsf{T}$ precisely when two given programs are equivalent on halting computations. We show that virtually any variant of propositional dynamic logic has $\Pi_1^1$-hard validity problem if it can express even just the equivalence of well-structured programs with the empty program \texttt{skip}. We also show, in these cases, that the set of propositional statements valid over finite models is not recursively enumerable, so there is not even an axiomatisation for finitely valid propositions.Comment: 8 page

Matching Subsequences in Trees

Given two rooted, labeled trees $P$ and $T$ the tree path subsequence problem is to determine which paths in $P$ are subsequences of which paths in $T$. Here a path begins at the root and ends at a leaf. In this paper we propose this problem as a useful query primitive for XML data, and provide new algorithms improving the previously best known time and space bounds.Comment: Minor correction of typos, et

On the testability of SDL specifications

The problem of testing from an SDL specification is often complicated by the presence of infeasible paths. This paper introduces an approach for transforming a class of SDL specification in order to eliminate or reduce the infeasible path problem. This approach is divided into two phases in order to aid generality. First the SDL specification is rewritten to create a normal form extended finite state machine (NF-EFSM). This NF-EFSM is then expanded in order to produce a state machine in which the test criterion may be satisfied using paths that are known to be feasible. The expansion process is guaranteed to terminate. Where the expansion process may lead to an excessively large state machine, this process may be terminated early and feasible paths added. The approach is illustrated through being applied to the Initiator process of the Inres protocol

Fast Arc-Annotated Subsequence Matching in Linear Space

An arc-annotated string is a string of characters, called bases, augmented with a set of pairs, called arcs, each connecting two bases. Given arc-annotated strings $P$ and $Q$ the arc-preserving subsequence problem is to determine if $P$ can be obtained from $Q$ by deleting bases from $Q$. Whenever a base is deleted any arc with an endpoint in that base is also deleted. Arc-annotated strings where the arcs are ``nested'' are a natural model of RNA molecules that captures both the primary and secondary structure of these. The arc-preserving subsequence problem for nested arc-annotated strings is basic primitive for investigating the function of RNA molecules. Gramm et al. [ACM Trans. Algorithms 2006] gave an algorithm for this problem using $O(nm)$ time and space, where $m$ and $n$ are the lengths of $P$ and $Q$, respectively. In this paper we present a new algorithm using $O(nm)$ time and $O(n + m)$ space, thereby matching the previous time bound while significantly reducing the space from a quadratic term to linear. This is essential to process large RNA molecules where the space is likely to be a bottleneck. To obtain our result we introduce several novel ideas which may be of independent interest for related problems on arc-annotated strings.Comment: To appear in Algoritmic

New onset or relapsing neuromyelitis optica temporally associated with SARS-CoV-2 infection and COVID-19 vaccination: a systematic review

BackgroundNeuromyelitis optica spectrum disorder (NMOSD) is a rare chronic neuroinflammatory autoimmune condition. Since the onset of the COVID-19 pandemic, there have been reports of NMOSD clinical manifestations following both SARS-CoV-2 infections and COVID-19 vaccinations.ObjectiveThis study aims to systematically review the published literature of NMOSD clinical manifestations associated with SARS-CoV-2 infections and COVID-19 vaccinations.MethodsA Boolean search of the medical literature was conducted between December 1, 2019 to September 1, 2022, utilizing Medline, Cochrane Library, Embase, Trip Database, Clinicaltrials.gov, Scopus, and Web of Science databases. Articles were collated and managed on Covidence® software. The authors independently appraised the articles for meeting study criteria and followed PRISMA guidelines. The literature search included all case reports and case series that met study criteria and involved NMOSD following either the SARS-CoV-2 infection or the COVID-19 vaccination.ResultsA total of 702 articles were imported for screening. After removing 352 duplicates and 313 articles based on exclusion criteria, 34 articles were analyzed. A total of 41 cases were selected, including 15 patients that developed new onset NMOSD following a SARS-CoV-2 infection, 21 patients that developed de novo NMOSD following COVID-19 vaccination, 3 patients with known NMOSD that experienced a relapse following vaccination, and 2 patients with presumed Multiple Sclerosis (MS) that was unmasked as NMOSD post-vaccination. There was a female preponderance of 76% among all NMOSD cases. The median time interval between the initial SARS-CoV-2 infection symptoms and NMOSD symptom onset was 14  days (range 3–120  days) and the median interval between COVID-19 vaccination and onset of NMO symptoms was 10  days (range 1 to 97  days). Transverse myelitis was the most common neurological manifestation in all patient groups (27/41). Management encompassed acute treatments such as high dose intravenous methylprednisolone, plasmapheresis, and intravenous immunoglobulin (IVIG) and maintenance immunotherapies. The majority of patients experienced a favorable outcome with complete or partial recovery, but 3 patients died.ConclusionThis systematic review suggests that there is an association between NMOSD and SARS-CoV-2 infections and COVID-19 vaccinations. This association requires further study using quantitative epidemiological assessments in a large population to better quantify the risk

Development of dependable controllers in the context of machines design

Proceedings of ICMD 2013In the domain of machines' design, one of the most important issues to solve is related with the controller's design, mainly, guaranteeing that the machine will behave as expected. In order to achieve a dependable controller, some steps can be considered, such as the formalization of its specification - before being translated to the program that will be inserted in the controller device - and the respective analysis and verification. Nowadays, some formal analysis techniques, such as formal verification, are used to achieve this purpose. The dependability of a controller, however, is impacted by its execution context. This paper proposes an approach for the formal verification of the specification of mechatronic system's controllers, which considers, on the formal verification tasks, the behavior of the plant and the behavior of the Human Machine Interface of the Mechatronic system. Some conclusions are extrapolated for other systems of the same kind

Evaluation of a magnetic resonance-compatible dentoalveolar tactile stimulus device

<p>Abstract</p> <p>Background</p> <p>Few methods exist to study central nervous system processes following dentoalveolar tactile stimulation using functional magnetic resonance imaging (fMRI), likely due to inherent technical difficulties. Our primary goal was to develop and perform feasibility testing of a novel device capable of delivering valid and reliable dentoalveolar stimuli at dental chair-side and during MRI. Details of a device designed to deliver dentoalveolar dynamic pressure stimuli are described. Device testing took place in three settings: a) laboratory testing to assess range of stimulus force intensities, b) dental chair-side to assess reliability, validity and discriminant ability in force-pain relationship; and c) MRI to evaluate magnetic compatibility and ability to evoke brain activation in painfree subjects similar to those described in the literature.</p> <p>Results</p> <p>A novel device capable of delivering valid and reliable dentoalveolar somatosensory stimulation was developed (ICC = 0.89, 0.78-1 [95% CI]). Psychophysical data analysis showed high discriminant ability in differentiating painfree controls from cases with chronic dentoalveolar pain related to deafferenting dental procedures (sensitivity = 100%, specificity = 86.7%, area under ROC curve = 0.99). FMRI results of dentoalveolar dynamic pressure pain in painfree subjects revealed activation of brain areas typically associated with acute pain processing including thalamus, primary/secondary somatosensory, insular and prefrontal cortex.</p> <p>Conclusions</p> <p>A novel psychophysical method to deliver dynamic dentoalveolar pressure stimulation was developed and validated, allowing non-invasive MRI-based exploration of central nervous system function in response to intraoral somatosensation.</p> <p>Background</p> <p>The organization of the trigeminal system is unique as it provides somatosensory innervation to the face, masticatory and oral structures, the majority of the intracranial contents <abbrgrp><abbr bid="B1">1</abbr></abbrgrp> and to specialized structures (tongue, nasal mucosa, auricle, tympanic membrane, cornea and part of the conjunctiva) <abbrgrp><abbr bid="B2">2</abbr></abbrgrp>. Somatic sensory information transmitted by the trigeminal nerve is crucial for normal orofacial function; however, the mechanisms of many chronic pain conditions affecting areas innervated by this sensory system are not well understood <abbrgrp><abbr bid="B3">3</abbr><abbr bid="B4">4</abbr><abbr bid="B5">5</abbr></abbrgrp>. The clinical presentation of chronic intraoral pain in the area of a tooth or in a site formally occupied by a tooth with no clinical or radiological signs of pathology, referred to as atypical odontalgia (AO) <abbrgrp><abbr bid="B6">6</abbr><abbr bid="B7">7</abbr></abbrgrp>, is one such chronic pain condition of particular interest to dentists that is difficult to diagnose and manage. Recent research suggests both peripheral and central nervous system mechanisms being involved in AO pathophysiology <abbrgrp><abbr bid="B8">8</abbr><abbr bid="B9">9</abbr><abbr bid="B10">10</abbr></abbrgrp>, but the majority of mechanism-based research of patients with AO has focused on the "peripheral aspect" <abbrgrp><abbr bid="B7">7</abbr></abbrgrp>.</p> <p>Functional magnetic resonance imaging (fMRI) is an established research technique to study the central aspects of pain <abbrgrp><abbr bid="B11">11</abbr></abbrgrp>. Of existing neuroimaging techniques, fMRI provides good spatial resolution of cortical and subcortical structures critical in the processing of nociception, acceptable temporal resolution, does not involve ionizing radiation, and can be performed using most MRI systems that already exist in research centers and the community. For these reasons, we sought to develop a protocol that allows us to use this tool to investigate the central mechanisms involved in the processes of intraoral pain arising from the dentoalveolar region. Using this device, our long-term objective is to improve our understanding of the underlying mechanisms of persistent dentoalveolar pain.</p> <p>In the past few years several studies used fMRI to investigate the human trigeminal system <abbrgrp><abbr bid="B12">12</abbr><abbr bid="B13">13</abbr></abbrgrp>, with a limited subset focusing on intraoral stimulation - specifically on the dentoalveolar processes, such as lip, tongue and teeth stimulation <abbrgrp><abbr bid="B14">14</abbr></abbrgrp> or only teeth <abbrgrp><abbr bid="B15">15</abbr><abbr bid="B16">16</abbr><abbr bid="B17">17</abbr></abbrgrp>. Some reasons for scarce literature on this topic may be the technical challenges involved in delivering facial/intraoral stimulation inside a MR scanner <abbrgrp><abbr bid="B17">17</abbr><abbr bid="B18">18</abbr></abbrgrp>: possibility of magnetic interference, detriment of image quality, subject discomfort and reduced working space between the subject's head and the radiofrequency coil. As a consequence a MR-compatible device would need to not only overcome these challenges but also be capable of delivering a controlled and reproducible stimuli <abbrgrp><abbr bid="B19">19</abbr></abbrgrp>, as reliability/reproducibility is a necessary feature of sensory testing <abbrgrp><abbr bid="B20">20</abbr></abbrgrp>.</p> <p>Existing MR-compatible methods of dentoalveolar stimulation are limited and do not adequately deliver stimuli across a range of non-painful to painful intensities and/or cannot be adjusted to reach posterior aspects of the dentoalveolar region. Therefore our goal was to develop and test the feasibility of a device able to: 1) provide reliable and valid dentoalveolar stimuli, 2) deliver such stimulation within the restricted space of an MR head coil, 3) be compatible for use within an MR environment, and 4) produce brain activation in painfree controls consistent to those observed by others using fMRI.</p

String Indexing for Patterns with Wildcards

We consider the problem of indexing a string $t$ of length $n$ to report the occurrences of a query pattern $p$ containing $m$ characters and $j$ wildcards. Let $occ$ be the number of occurrences of $p$ in $t$, and $\sigma$ the size of the alphabet. We obtain the following results. - A linear space index with query time $O(m+\sigma^j \log \log n + occ)$. This significantly improves the previously best known linear space index by Lam et al. [ISAAC 2007], which requires query time $\Theta(jn)$ in the worst case. - An index with query time $O(m+j+occ)$ using space $O(\sigma^{k^2} n \log^k \log n)$, where $k$ is the maximum number of wildcards allowed in the pattern. This is the first non-trivial bound with this query time. - A time-space trade-off, generalizing the index by Cole et al. [STOC 2004]. We also show that these indexes can be generalized to allow variable length gaps in the pattern. Our results are obtained using a novel combination of well-known and new techniques, which could be of independent interest

Drawing Trees with Perfect Angular Resolution and Polynomial Area

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2{\pi}/d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.Comment: 30 pages, 17 figure