Twisting Goppa Codes

10 pagesInternational audienceThe aim of this paper is to explain how, starting from a Goppa code C(X, G, P1, . . . , Pn) and a cyclic covering π : Y → X of degree m, oone can twist the initial code to another one C(X, G + Dχ , P1, . . . , Pn), where Dχ is a non-principal degree 0 divisor on X associated to a character χ of Gal(Y /X), in the hope that X (G + Dχ) > X (G). We give, using a MAGMA program, several examples where this occurs, and where both the initial and twisted codes have same minimum distance, so that initial codes have been improved

TUNNEL PORTAL INSTABILITY IN LANDSLIDE AREA AND REMEDIAL SOLUTION: A CASE STUDY

The construction of tunnel portals in mountainous or slope areas often involves problems, which are closely related to factors, such as slope topography, geology, geotechnics, construction geometry and the tunnel excavation method. The activation of landslides or the acceleration of these events is one of the main challenges faced in the construction of tunnel portals. In this paper, we address the instability problem in Sabzkuh tunnel portal that has been excavated with a complex geological profile and high seismicity in Iran’s High Zagros region. The complexity and intense heterogeneity in geological formations, land acquisition problems and the lack of appropriate monitoring programs led to the instability of the tunnel portal. The excavation process started without applying appropriate techniques for a ground stabilization. The use of inappropriate tunnel excavation methods for this unstable geological structure resulted in an activation of an old Solaghan fault and several collapses in the tunnel. Crossing the collapsed areas and reinforcing the tunnel portal took about 7 months and imposed heavy costs on the project. This case study deals with the importance of the choice of the site location, ground and underground monitoring, analysing and summarizing the collected data in order to prepare a geological model before and during the construction process

λ∞\lambda_\infty & Maximum Variance Embedding: Measuring and Optimizing Connectivity of A Graph Metric

Bobkov, Houdr\'e, and the last author [2000] introduced a Poincar\'e-type functional parameter, $\lambda_\infty$, of a graph and related it to connectivity of the graph via Cheeger-type inequalities. A work by the second author, Raghavendra, and Vempala [2013] related the complexity of $\lambda_\infty$ to the so-called small-set expansion (SSE) problem and further set forth the desiderata for NP-hardness of this optimization problem. We confirm the conjecture that computing $\lambda_\infty$ is NP-hard for weighted trees. Beyond measuring connectivity in many applications we want to optimize it. This, via convex duality, leads to a problem in machine learning known as the Maximum Variance Embedding (MVE). The output is a function from vertices to a low dim Euclidean space, subject to bounds on Euclidean distances between neighbors. The objective is to maximize output variance. Special cases of MVE into $n$ and $1$ dims lead to absolute algebraic connectivity [1990] and spread constant [1998], that measure connectivity of the graph and its Cartesian $n$-power, respectively. MVE has other applications in measuring diffusion speed and robustness of networks, clustering, and dimension reduction. We show that computing MVE in tree-width dims is NP-hard, while only one additional dim beyond width of a given tree-decomposition makes the problem in P. We show that MVE of a tree in 2 dims defines a non-convex yet benign optimization landscape, i.e., local=global optima. We further develop a linear time combinatorial algorithm for this case. Finally, we denote approximate Maximum Variance Embedding is tractable in significantly lower dims. For trees and general graphs, for which Maximum Variance Embedding cannot be solved in less than $2$ and $\Omega(n)$ dims, we provide $1+\varepsilon$ approximation algorithms for embedding into $1$ and $O(\log n /\varepsilon^2)$ dims, respectively

Bridging Classical and Quantum with SDP initialized warm-starts for QAOA

We study the Quantum Approximate Optimization Algorithm (QAOA) in the context of the Max-Cut problem. Near-term (noisy) quantum devices are only able to (accurately) execute QAOA at low circuit depths while QAOA requires a relatively high circuit-depth in order to "see" the whole graph. We introduce a classical pre-processing step that initializes QAOA with a biased superposition of all possible cuts in the graph, referred to as a warm-start. In particular, our initialization informs QAOA by a solution to a low-rank semidefinite programming relaxation of the Max-Cut problem. Our experimental results show that this variant of QAOA, called QAOA-Warm, is able to outperform standard QAOA on lower circuit depths with less training time (in the optimization stage for QAOA's variational parameters). We provide experimental evidence as well as theoretical intuition on performance of the proposed framework

Hardness and Approximation of Submodular Minimum Linear Ordering Problems

The minimum linear ordering problem (MLOP) generalizes well-known combinatorial optimization problems such as minimum linear arrangement and minimum sum set cover. MLOP seeks to minimize an aggregated cost $f(\cdot)$ due to an ordering $\sigma$ of the items (say $[n]$), i.e., $\min_{\sigma} \sum_{i\in [n]} f(E_{i,\sigma})$, where $E_{i,\sigma}$ is the set of items mapped by $\sigma$ to indices $[i]$. Despite an extensive literature on MLOP variants and approximations for these, it was unclear whether the graphic matroid MLOP was NP-hard. We settle this question through non-trivial reductions from mininimum latency vertex cover and minimum sum vertex cover problems. We further propose a new combinatorial algorithm for approximating monotone submodular MLOP, using the theory of principal partitions. This is in contrast to the rounding algorithm by Iwata, Tetali, and Tripathi [ITT2012], using Lov\'asz extension of submodular functions. We show a $(2-\frac{1+\ell_{f}}{1+|E|})$-approximation for monotone submodular MLOP where $\ell_{f}=\frac{f(E)}{\max_{x\in E}f(\{x\})}$ satisfies $1 \leq \ell_f \leq |E|$. Our theory provides new approximation bounds for special cases of the problem, in particular a $(2-\frac{1+r(E)}{1+|E|})$-approximation for the matroid MLOP, where $f = r$ is the rank function of a matroid. We further show that minimum latency vertex cover (MLVC) is $\frac{4}{3}$-approximable, by which we also lower bound the integrality gap of its natural LP relaxation, which might be of independent interest

Interference Alignment — Practical Challenges and Test-bed Implementation

Data traffic over wireless communication networks has experienced a tremendous growth in the last decade, and it is predicted to exponentially increase in the next decades. Enabling future wireless networks to fulfill this expectation is a challenging task both due to the scarcity of radio resources (e.g. spectrum and energy), and also the inherent characteristics of the wireless transmission medium. Wireless transmission is in general subject to two phenomena: fading and interference. The elegant interference alignment concept reveals that with proper transmission signalling design, different interference signals can in fact be aligned together, such that more radio resources can be assigned to the desired transmission. Although interference alignment can achieve a larger data rate compared to orthogonal transmission strategies, several challenges should be addressed to enable the deployment of this technique in future wireless networks For instance, to perform interference alignment, normally, global channel state information (CSI) is required to be perfectly known at all terminals. Clearly, acquiring such channel knowledge is a challenging problem in practice and proper channel training and channel state feedback techniques need to be deployed. In addition, since the channels are time-varying proper adaptive transmission is needed. This chapter review recent advances in practical aspects of interference alignment. It also presents recent test-bed implementations of signal processing algorithms for the realization of interference alignment.Comment: Book Chapter accepted for publication in the book entitled: Contemporary Issues in Wireless Communications, ISBN: 978-953-51-4101-3, Khatib, M. (Ed.), to be published by INTECH Publishers. Expected month of publication: November 201

Latitude, Vitamin D, Melatonin, and Gut Microbiota Act in Concert to Initiate Multiple Sclerosis: A New Mechanistic Pathway

Multiple sclerosis (MS) is an inflammatory demyelinating disease of the central nervous system (CNS). While the etiology of MS is still largely unknown, scientists believe that the interaction of several endogenous and exogenous factors may be involved in this disease. Epidemiologists have seen an increased prevalence of MS in countries at high latitudes, where the sunlight is limited and where the populations have vitamin D deficiency and high melatonin levels. Although the functions and synthesis of vitamin D and melatonin are contrary to each other, both are involved in the immune system. While melatonin synthesis is affected by light, vitamin D deficiency may be involved in melatonin secretion. On the other hand, vitamin D deficiency reduces intestinal calcium absorption leading to gut stasis and subsequently increasing gut permeability. The latter allows gut microbiota to transfer more endotoxins such as lipopolysaccharides (LPS) into the blood. LPS stimulates the production of inflammatory cytokines within the CNS, especially the pineal gland. This review summarizes the current findings on the correlation between latitude, sunlight and vitamin D, and details their effects on intestinal calcium absorption, gut microbiota and neuroinflammatory mediators in MS. We also propose a new mechanistic pathway for the initiation of MS

Improved approximations for min sum vertex cover and generalized min sum set cover

We study the generalized min sum set cover (GMSSC) problem, wherein given a collection of hyperedges E with arbitrary covering requirements {ke ∈ Z+ : e ∈ E}, the goal is to find an ordering of the vertices to minimize the total cover time of the hyperedges; a hyperedge e is considered covered by the first time when ke many of its vertices appear in the ordering. We give a 4.642 approximation algorithm for GMSSC, coming close to the best possible bound of 4, already for the classical special case (with all ke = 1) of min sum set cover (MSSC) studied by Feige, Lovász and Tetali [11], and improving upon the previous best known bound of 12.4 due to Im, Sviridenko and van der Zwaan [20]. Our algorithm is based on transforming the LP solution by a suitable kernel and applying randomized rounding. This also gives an LP-based 4 approximation for MSSC. As part of the analysis of our algorithm, we also derive an inequality on the lower tail of a sum of independent Bernoulli random variables, which might be of independent interest and broader utility. Another well-known special case is the min sum vertex cover (MSVC) problem, in which the input hypergraph is a graph (i.e., |e| = 2) and ke = 1, for every edge e ∈ E. We give a 16/9 ' 1.778 approximation for MSVC, and show a matching integrality gap for the natural LP relaxation. This improves upon the previous best 1.999946 approximation of Barenholz, Feige and Peleg [6]. (The claimed 1.79 approximation result of Iwata, Tetali and Tripathi [21] for the MSVC turned out have an unfortunate, seemingly unfixable, mistake in it.) Finally, we revisit MSSC and consider the lp norm of cover-time of the hyperedges. Using a dual fitting argument, we show that the natural greedy algorithm simultaneously achieves approximation guarantees of (p + 1)1+1/p, for all p ≥ 1, giving another proof of the result of Golovin, Gupta, Kumar and Tangwongsan [13], and showing its tightness up to NP-hardness. For p = 1, this gives yet another proof of the 4 approximation for MSSC

Melatonin Therapy Modulates Cerebral Metabolism and Enhances Remyelination by Increasing PDK4 in a Mouse Model of Multiple Sclerosis

Metabolic disturbances have been implicated in demyelinating diseases including multiple sclerosis (MS). Melatonin, a naturally occurring hormone, has emerged as a potent neuroprotective candidate to reduce myelin loss and improve MS outcomes. In this study, we evaluated the effect of melatonin, at both physiological and pharmacological doses, on oligodendrocytes metabolism in an experimental autoimmune encephalomyelitis (EAE) mouse model of MS. Results showed that melatonin decreased neurological disability scores and enhanced remyelination, significantly increasing myelin protein levels including MBP, MOG, and MOBP. In addition, melatonin attenuated inflammation by reducing pro-inflammatory cytokines (IL-1β and TNF-α) and increasing anti-inflammatory cytokines (IL-4 and IL-10). Moreover, melatonin significantly increased brain concentrations of lactate, N-acetylaspartate (NAA), and 3-hydroxy-3-methylglutaryl-coenzyme-A reductase (HMGCR). Pyruvate dehydrogenase kinase-4 (PDK-4) mRNA and protein expression levels were also increased in melatonin-treated, compared to untreated EAE mice. However, melatonin significantly inhibited active and total pyruvate dehydrogenase complex (PDC), an enzyme under the control of PDK4. In summary, although PDC activity was reduced by melatonin, it caused a reduction in inflammatory mediators while stimulating oligodendrogenesis, suggesting that oligodendrocytes are forced to use an alternative pathway to synthesize fatty acids for remyelination. We propose that combining melatonin and PDK inhibitors may provide greater benefits for MS patients than the use of melatonin therapy alone