List decoding of noisy Reed-Muller-like codes

First- and second-order Reed-Muller (RM(1) and RM(2), respectively) codes are two fundamental error-correcting codes which arise in communication as well as in probabilistically-checkable proofs and learning. In this paper, we take the first steps toward extending the quick randomized decoding tools of RM(1) into the realm of quadratic binary and, equivalently, Z_4 codes. Our main algorithmic result is an extension of the RM(1) techniques from Goldreich-Levin and Kushilevitz-Mansour algorithms to the Hankel code, a code between RM(1) and RM(2). That is, given signal s of length N, we find a list that is a superset of all Hankel codewords phi with dot product to s at least (1/sqrt(k)) times the norm of s, in time polynomial in k and log(N). We also give a new and simple formulation of a known Kerdock code as a subcode of the Hankel code. As a corollary, we can list-decode Kerdock, too. Also, we get a quick algorithm for finding a sparse Kerdock approximation. That is, for k small compared with 1/sqrt{N} and for epsilon > 0, we find, in time polynomial in (k log(N)/epsilon), a k-Kerdock-term approximation s~ to s with Euclidean error at most the factor (1+epsilon+O(k^2/sqrt{N})) times that of the best such approximation

Algorithmic linear dimension reduction in the l_1 norm for sparse vectors

This paper develops a new method for recovering m-sparse signals that is simultaneously uniform and quick. We present a reconstruction algorithm whose run time, O(m log^2(m) log^2(d)), is sublinear in the length d of the signal. The reconstruction error is within a logarithmic factor (in m) of the optimal m-term approximation error in l_1. In particular, the algorithm recovers m-sparse signals perfectly and noisy signals are recovered with polylogarithmic distortion. Our algorithm makes O(m log^2 (d)) measurements, which is within a logarithmic factor of optimal. We also present a small-space implementation of the algorithm. These sketching techniques and the corresponding reconstruction algorithms provide an algorithmic dimension reduction in the l_1 norm. In particular, vectors of support m in dimension d can be linearly embedded into O(m log^2 d) dimensions with polylogarithmic distortion. We can reconstruct a vector from its low-dimensional sketch in time O(m log^2(m) log^2(d)). Furthermore, this reconstruction is stable and robust under small perturbations

Математическое моделирование взаимодействия верхового лесного пожара с противопожарным разрывом конечных размеров

Analysis of dependence of the critical dimensions of fire ruptures on the main characteristics of forests and wind speed. As a result of the numerical integration of fields was obtained the temperature distribution, oxygen concentration and volatile combustible pyrolysis products

Intravitreal bevacizumab for the treatment of macular oedema secondary to branch retinal vein occlusion

Purpose: To evaluate the effect of intravitreal bevacizumab (Avastin) injections on visual acuity (VA) and foveal retinal thickness in patients with macular oedema secondary to branch retinal vein occlusion.Methods: A prospective, non-comparative, consecutive, interventional case series of 34 patients. Patients received repeated intravitreal injections of 1.25 mg bevacizumab. Main outcome measures were VA (Snellen charts and ETDRS) and retinal thickness (optical coherence tomography measurements) in a follow-up period of 6 months.Results: Patients presented at a mean age of 69 years (range 44--86). Mean duration of symptoms was 40 weeks (range 1--300). Mean (SD) VA at baseline was 0.79 (0.39) logMAR, improving to 0.51 (0.34) logMAR at 6 months (p = 0.009). Mean number of letters on the ETDRS chart at baseline was 45.3 (19.0), improving to 60.6 (19.9) at 6 months (p = 0.003). Mean (SD) retinal thickness at baseline was 474 (120) \textgreekmm, declining to 316 (41) \textgreekmm at 6 months.Conclusion: Intravitreal injection of 1.25 mg bevacizumb appears to be an effective treatment option for branch retinal vein occlusion

Super-resolution imaging and estimation of protein copy numbers at single synapses with DNA-PAINT

In the brain, the strength of each individual synapse is defined by the complement of proteins present or the "local proteome." Activity-dependent changes in synaptic strength are the result of changes in this local proteome and posttranslational protein modifications. Although most synaptic proteins have been identified, we still know little about protein copy numbers in individual synapses and variations between synapses. We use DNA-point accumulation for imaging in nanoscale topography as a single-molecule super-resolution imaging technique to visualize and quantify protein copy numbers in single synapses. The imaging technique provides near-molecular spatial resolution, is unaffected by photobleaching, enables imaging of large field of views, and provides quantitative molecular information. We demonstrate these benefits by accessing copy numbers of surface AMPA-type receptors at single synapses of rat hippocampal neurons along dendritic segments

Mythical Thinking, Scientific Discourses and Research Dissemination

This article focuses on some principles for understanding. By taking Anna Mikulak’s article “Mismatches between ‘scientific’ and ‘non-scientific’ ways of knowing and their contributions to public understanding of science” (IPBS 2011) as a point of departure, the idea of demarcation criteria for scientific and non-scientific discourses is addressed. Yet this is juxtaposed with mythical thinking, which is supposed to be the most salient trait of non-scientific discourses. The author demonstrates how the most widespread demarcation criterion, the criterion of verification, is self-contradictory, not only when it comes to logic, but also in the achievement of isolating natural sciences from other forms of knowledge. According to Aristotle induction is a rhetorical device and as far as scientific statements are based on inductive inferences, they are relying on humanities, which rhetoric is a part of. Yet induction also has an empirical component by being based on sense-impressions, which is not a part of the rhetoric, but the psychology. Also the myths are understood in a rhetorical (Lévi-Strauss) and a psychological (Cassirer) perspective. Thus it is argued that both scientific and non-scientific discourses can be mythical

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

We study in detail the ratchet-like dynamics of topological solitons in homogeneous nonlinear Klein-Gordon systems driven by a bi-harmonic force. By using a collective coordinate approach with two degrees of freedom, namely the center of the soliton, $X(t)$, and its width, $l(t)$, we show, first, that energy is inhomogeneously pumped into the system, generating as result a directed motion; and, second, that the breaking of the time shift symmetry gives rise to a resonance mechanism that takes place whenever the width $l(t)$ oscillates with at least one frequency of the external ac force. In addition, we show that for the appearance of soliton ratchets, it is also necesary to break the time-reversal symmetry. We analyze in detail the effects of dissipation in the system, calculating the average velocity of the soliton as a function of the ac force and the damping. We find current reversal phenomena depending on the parameter choice and discuss the important role played by the phases of the ac force. Our analytical calculations are confirmed by numerical simulations of the full partial differential equations of the sine-Gordon and $\phi^4$ systems, which are seen to exhibit the same qualitative behavior. Our results are in agreement with recent experimental work on dissipation induced symmetry breaking.Comment: Minor corrections, several references added, accepted for publication in Chao

Forest structure, stand composition, and climate-growth response in montane forests of Jiuzhaigou National Nature Reserve, China.

Montane forests of western China provide an opportunity to establish baseline studies for climate change. The region is being impacted by climate change, air pollution, and significant human impacts from tourism. We analyzed forest stand structure and climate-growth relationships from Jiuzhaigou National Nature Reserve in northwestern Sichuan province, along the eastern edge of the Tibetan plateau. We conducted a survey to characterize forest stand diversity and structure in plots occurring between 2050 and 3350 m in elevation. We also evaluated seedling and sapling recruitment and tree-ring data from four conifer species to assess: 1) whether the forest appears in transition toward increased hardwood composition; 2) if conifers appear stressed by recent climate change relative to hardwoods; and 3) how growth of four dominant species responds to recent climate. Our study is complicated by clear evidence of 20(th) century timber extraction. Focusing on regions lacking evidence of logging, we found a diverse suite of conifers (Pinus, Abies, Juniperus, Picea, and Larix) strongly dominate the forest overstory. We found population size structures for most conifer tree species to be consistent with self-replacement and not providing evidence of shifting composition toward hardwoods. Climate-growth analyses indicate increased growth with cool temperatures in summer and fall. Warmer temperatures during the growing season could negatively impact conifer growth, indicating possible seasonal climate water deficit as a constraint on growth. In contrast, however, we found little relationship to seasonal precipitation. Projected warming does not yet have a discernible signal on trends in tree growth rates, but slower growth with warmer growing season climates suggests reduced potential future forest growth

The Effects of Negative Legacies on the Adjustment of Parentally Bereaved Children and Adolescents

This is a report of a qualitative analysis of a sample of bereaved families in which one parent died and in which children scored in the clinical range on the Child Behavior Check List. The purpose of this analysis was to learn more about the lives of these children. They were considered to be at risk of developing emotional and behavioral problems associated with the death. We discovered that many of these “high risk” children had a continuing bond with the deceased that was primarily negative and troubling for them in contrast to a comparison group of children not at risk from the same study. Five types of legacies, not mutually exclusive, were identified: health related, role related, personal qualities, legacy of blame, and an emotional legacy. Coping behavior on the part of the surviving parent seemed to make a difference in whether or not a legacy was experienced as negative