Derandomization via Symmetric Polytopes: Poly-Time Factorization of Certain Sparse Polynomials

More than three decades ago, after a series of results, Kaltofen and Trager (J. Symb. Comput. 1990) designed a randomized polynomial time algorithm for factorization of multivariate circuits. Derandomizing this algorithm, even for restricted circuit classes, is an important open problem. In particular, the case of s-sparse polynomials, having individual degree d = O(1), is very well-studied (Shpilka, Volkovich ICALP\u2710; Volkovich RANDOM\u2717; Bhargava, Saraf and Volkovich FOCS\u2718, JACM\u2720). We give a complete derandomization for this class assuming that the input is a symmetric polynomial over rationals. Generally, we prove an s^poly(d)-sparsity bound for the factors of symmetric polynomials over any field. This characterizes the known worst-case examples of sparsity blow-up for sparse polynomial factoring. To factor f, we use techniques from convex geometry and exploit symmetry (only) in the Newton polytope of f. We prove a crucial result about convex polytopes, by introducing the concept of "low min-entropy", which might also be of independent interest

A review on the role of emerging anthropogenic activities in environmental degradation and emphasis on their mitigation

Environmental degradation is the deterioration of natural resources such as air, water, soil, flora, fauna, and all other living and non-living component of the planet earth. There are two main reasons for environmental degradation i.e. anthropogenic causes like industrialization, overpopulation, deforestation, mining, etc. and natural causes like flood, landslide, desertification, temperatures, etc. Nowadays, the demand for natural resources is increase due to the exceeding population. To fulfill the demand of humans, over exploration of the natural resources in carrying out, due to this they are under pressure. The anthropogenic activities disturbed and degraded the environmental component such as the atmosphere, hydrosphere, biosphere, and lithosphere. All the environmental component is linked together if one is disturbed than its disturbed the other one also. However, in this paper, we discussed the anthropogenic activities that affect the environmental component directly or indirectly and we also suggested the recommendation and mitigation measures to sustain the environmental component developed by the agencies and policymaker

An analysis of working women in Bareilly, Uttar Pradesh in context to work life balance

Economic and societal factors have altered the roles and obligations of women across the globe. Thus, women who work are under great pressure to achieve professional success on par with their male colleagues while retaining an active role in their home life at the same time. Because of their increasing responsibilities, many working women are finding it more difficult to take time for themselves. Today's knowledge-based culture is overburdened with stress due to the proliferation of high-tech gadgets like smartphones, laptops, and other portable computing devices. All three aspects of a person's health are affected by this. In order to maintain a high standard of living while working, women must learn to strike a WLB. Women in the workforce have particular challenges in juggling their professional and personal lives. These are the questions that we want to answer with this study. This study found that a broad variety of factors affected married working women's ability to maintain a healthy WLB. The Industrial Society's handbook on work–life balance was used for this study. In a survey of working women in Bareilly,Uttar Pradesh, some shocking findings were found on the difficulties they encounter in juggling job and family obligations

Warning leak of intracranial aneurysm masquerading as sinus node dysfunction: A case report

We describe the successful endovascular repair of an intracranial aneurysm causing subarachnoid hemorrhage in a 62-year-old man, who was initially diagnosed and treated as a case of symptomatic sinus bradycardia. The aim of this report and following discussion is to discuss the subtle warning signs of intracranial aneurysm that may masquerade as sinus node dysfunction

Radiographic evaluation of tonsilloliths in digital panoramic radiography – An institutional-based retrospective study

Background: Tonsilloliths/tonsillitis are calcifications that can be found in the lymphoid tissues of the posterior nasopharyngeal wall and the palatine tonsil. The majority of tonsilloliths are tiny, asymptomatic, and are typically discovered by accident during routine dental radiography. Objective: To assess the prevalence and characteristics of tonsilloliths in digital panoramic radiographs. Materials and Methods: The study population showed the presence of tonsilloliths in 400 out of 1000 digital panoramic radiographs screened. Results: Gender distribution of tonsillitis showed 66.5% female and 33.5% male patients. The age range was between 21-69 years with 41–50 years showing a maximum of 25% tonsilloliths. They were found unilaterally in 236 and bilaterally in 164 subjects. The most common location was in the bottom third of the mandibular body (61%), with more tonsillitis on the right side. Females had 44.4% more tonsilitis present unilaterally. The association of tonsilloliths between different age groups revealed highly significant values for the presence, quantity, and side involvement. Conclusion: Tonsilloliths are a frequent incidental finding in radiographs. They can be more easily found using panoramic radiography

Ligand migration and hexacoordination in type 1 non-symbiotic rice hemoglobin

Type 1 non-symbiotic rice hemoglobin (rHb1) shows bis-histidyl heme hexacoordination and is capable of binding diatomic ligands reversibly. The biological function is as yet unclear, but the high oxygen affinity makes it unlikely to be involved in oxygen transport. In order to gain insight into possible physiological roles, we have studied CO rebinding kinetics after laser flash photolysis of rHb1 in solution and encapsulated in silica gel. CO rebinding to wt rHb1 in solution occurs through a fast geminate phase with no sign of rebinding from internal docking sites. Encapsulation in silica gel enhances migration to internal cavities. Site-directed mutagenesis of FB10, a residue known to have a key role in the regulation of hexacoordination and ligand affinity, resulted in substantial effects on the rebinding kinetics, partly inhibiting ligand exit to the solvent, enhancing geminate rebinding and enabling ligand migration within the internal cavities. The mutation of HE7, one of the histidyl residues involved in the hexacoordination, prevents hexacoordination, as expected, but also exposes ligand migration through a complex system of cavities

Evaluation of Mirasol pathogen reduction system by artificially contaminating platelet concentrates with Staphylococcus epidermidis: A pilot study from India

Background and Objectives: This study was conducted to assess the efficacy of Mirasol pathogen reduction system for platelets aimed at preventing bacterial regrowth by spiking buffy coat pooled platelets (BCPP) with clinically relevant load of Staphylococous epidermidis. Materials and Methods: BCPP units were prepared using Teruflex BP-kit with Imugard III-S-PL (Terumo BCT, Tokyo, Japan). Two BCPP units were pooled, of which 40 ml of negative control (NC) was removed. The remaining volume of the platelet unit was inoculated with clinically relevant load of bacteria (total of 30 CFU of S. epidermidis in 1 ml); following this the platelet unit was split into two parts. One part served as positive control (PC) and the other part was subjected to pathogen reduction technique (Mirasol PRT, CaridianBCT Biotechnologies, Lakewood, CO, USA). Bacterial detection was performed using BacT/ALERT system, controls after day 1 and day 7 following inoculation of bacteria and on day 7 for Mirasol-treated unit. Results: Of the 32 treatment cycles, 28 were valid and 4 were invalid. No regrowth was observed in 96.4% (27 of 28) after treatment with Mirasol pathogen reduction system. Of four invalid tests, on two instances the NC showed growth, whereas in other 2 no regrowth was detected in 7th day PC. Bacterial screening of PCs by BacT/ALERT after 24 h of incubation was 28.6%, whereas the effectiveness increased to 100% when incubated for 7 days. Conclusions: Mirasol system was effective in inactivating S.epidermidis when it was deliberately inoculated into BCPP at clinically relevant concentrations. Such systems may significantly improve blood safety by inactivating traditional and emerging transfusion-transmitted pathogens