Nearly Optimal Private Convolution

We study computing the convolution of a private input $x$ with a public input $h$, while satisfying the guarantees of $(\epsilon, \delta)$-differential privacy. Convolution is a fundamental operation, intimately related to Fourier Transforms. In our setting, the private input may represent a time series of sensitive events or a histogram of a database of confidential personal information. Convolution then captures important primitives including linear filtering, which is an essential tool in time series analysis, and aggregation queries on projections of the data. We give a nearly optimal algorithm for computing convolutions while satisfying $(\epsilon, \delta)$-differential privacy. Surprisingly, we follow the simple strategy of adding independent Laplacian noise to each Fourier coefficient and bounding the privacy loss using the composition theorem of Dwork, Rothblum, and Vadhan. We derive a closed form expression for the optimal noise to add to each Fourier coefficient using convex programming duality. Our algorithm is very efficient -- it is essentially no more computationally expensive than a Fast Fourier Transform. To prove near optimality, we use the recent discrepancy lowerbounds of Muthukrishnan and Nikolov and derive a spectral lower bound using a characterization of discrepancy in terms of determinants

Delineation of groundwater potential zones in the hilly topographic region of Serchhip, Mizoram, using Geospatial and analytical hierarchy process

Groundwater is the most important source of freshwater next to the surface water. Delineation of groundwater potential is critically essential, particularly in hilly complex topographic regions, where the surface water dries up during the dry season. The present study aimed to delineate groundwater potential areas to address the issue of water scarcity in the Serchhip district, Mizoram. The integration of different thematic layers such as lithology, Normalized Difference Vegetation Index (NDVI), rainfall, slope, soil texture, geomorphology, drainage density, lineament density and Topographic Wetness Index (TWI), the groundwater potential zone layers was prepared by Analytical Hierarchy Process (AHP) method. The groundwater potential zones (GWPZ) were classified into five: poor, fair, moderate, good, and excellent. The study revealed that the moderate-good zone occupied about 79.27 % (1126.77 km2), and the fair zone covered an area of about 9.52 % (135.3 km²), while the poor area was only 5.30 % (75.3 km²) out of the total study area (1421.5 km2). The demarcation of groundwater potential zones in Serchhip, Mizoram, served to combat water scarcity in mountainous areas. The amalgamation of geospatial data and AHP methodologies offered pivotal insights for the sustainable management of water resources, facilitating informed decision-making and conservation endeavours amidst the challenges posed by climate fluctuations and population expansion.  

Buckling of elastic circular plates with an elastically restrained edges against rotation and internal elastic ring support

The buckling of elastic circular plates with an internal elastic ring support and elastically restrained edges against rotation and simply supported is concerned. The classical plate theory is used to derive the governing differential equation. This work presents the existence of buckling mode switching with respect to the radius of internal elastic ring support. The plate may buckle in an axisymmetric mode in general, but when the radius of the ring support becomes small, the plate may buckle in an asymmetric mode. The cross-over ring support radius varies from 0.09891 to 0.1545 times the plate radius, depending on the rotational stiffness of the elastic restraint at the edges and elastic restraint of the ring. The optimum radius of the internal elastic ring support for maximum buckling load is also determined. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of rotational restraint, translational restraint of internal elastic ring support, Poisson’s ratio, and other boundary conditions on the buckling of uniform isotropic circular plates. The numerical results obtained are in good agreement with the previously published data.Розглянуто випучування пружної круглої пластинки з внутрішнім кріпленням у вигляді пружного кільця і зовнішньою границею, яка обмежує пружне обертання і є вільно опертою. Виведено диференціальні рівняння, що описують задачу, для чого використано класичну теорію пластинок. Запропоновано доведення існування перемикання на моду випучування в залежності від радіуса внутрішнього кільця. Пластинка може випучуватися, взагалі кажучи, за осесиметричною модою, але для малого радіуса кільця пластинка може випучуватися за неосесиметричною модою. Перехідне значення відношення радіуса кільця до радіуса пластинки змінюється від 0,9891 до 0,1545 в залежності від жорсткості кільця і обмеження на обертання на зовнішній границі пластинки. Також визначено максимальний радіус кільця, пов'язаний з максимальним значенням навантаження. Числові дані згруповані таким чином, що вони дозволяють зробити висновки щодо впливу обмеження на обертання, обмеження на поступальний рух кільця, коефіцієнта Пуассона та інших граничних умов на випучування однорідної круглої пластинки. Отримані числові результати добре узгоджуються з даними, опублікованими раніше

Analysis of Vibration Natural Frequencies of Rotationally Restrained and Simply Supported Circular Plate with Weakened Interior Circle Due to an Angular Crack

Получено точное решение для описания колебаний шарнирно закрепленной по внешнему краю круговой пластины с ограничением по вращению, которая ослаблена круговой трещиной. Рассчитаны частоты шести первых мод колебаний пластины для различных значений упругих характеристик шарнирного защемления, радиуса круговой трещины и степени ослабления пластины трещиной. Наличие трещины моделируется в виде фиктивного упругого закрепления пластины по линии трещины. Показано, что ослабление пластины трещиной приводит к снижению собственной частоты колебаний на 30%. Предполагается, что использование результатов точного решения является перспективным при оценке влияния трещины на колебания круговой пластины с внешним шарнирным закреплением и ограничением по вращению и верификации данных, полученных приближенными численными методами, включая метод конечных элементов.Отримано точний розв’язок для опису коливань шарнірно закріпленої по зовнішньому краю кругової пластини з обмеженням по обертанню, яка послаблена круговою тріщиною. Розраховано частоти шести перших мод коливань пластини для різних значень пружних характеристик шарнірного затиснення, радіуса кругової тріщини та міри послаблення пластини тріщиною. Наявність тріщини моделюється у вигляді фіктивного пружного закріплення пластини по лінії тріщини. Показано, що послаблення пластини тріщиною призводить до зниження власної частоти коливань на 30%. Припускається, що використання результатів точного розв’язку є перспективним при оцінці впливу тріщини на коливання кругової пластини із зовнішнім шарнірним закріпленням і обмеженням по обертанню та верифікації даних, що отримані наближеними числовими методами, включаючи з метод скінченних елементів

Efeitos da quitosana no desenvolvimento in vitro de videiras cv. merlot e no crescimento micelial do fungo elsinoe ampelina.

Objetivou-se, neste trabalho, avaliar o efeito da quitosana no desenvolvimento in vitro de plântulas de videira cv. Merlot e sua atividade antifúngica sobre Elsinoe ampelina. No primeiro experimento, explantes da cultivar Merlot foram transferidos para meio de cultura DSD1, acrescido das concentrações 0; 25; 50,100; 150 e 200 mg L-1 de quitosana. Após 90 dias de cultivo in vitro, as plântulas foram avaliadas quanto ao número de raízes e de folhas, porcentagem de enraizamento e brotação, comprimento de raízes e de parte aérea, massa fresca da planta. No segundo experimento, incorporou-se às concentrações 0, 60, 120, 180, 240 e 300 mg L-1 de quitosana ao meio BDA, onde inoculou-se o fungo. Posteriormente, avaliou-se o crescimento micelial aos 6 e 9 dias de incubação a 25º C no escuro. No primeiro experimento para as variáveis comprimento médio da parte aérea, massa fresca da planta inteira, porcentagem de enraizamento e porcentagem de estacas brotadas houve decréscimo linear em função das concentrações de quitosana. No segundo experimento, houve efeito linear negativo em função das concentrações crescentes de quitosana, sendo que a inibição do crescimento micelial foi de 81,7%, demonstrando o grande potencial do uso de quitosana no controle da antracnose da videira

Novel co-crystals of the nutraceutical sinapic acid

Sinapic acid (SA) is a nutraceutical with known anti-oxidant, anti-microbial, anti-inflammatory, anti-cancer, and anti-anxiety properties. Novel co-crystals of SA were prepared with co-formers belonging to the category of GRAS [isonicotinic acid (INC), nicotinamide (NIA)], non-GRAS [4-pyridinecarbonitrile (PYC)], and active pharmaceutical ingredients (APIs) [6-propyl-2-thiouracil (PTU)] list of compounds. Structural study based on the X-ray crystal structures revealed the intermolecular hydrogen-bonded interactions and molecular packing. The crystal structure of sinapic acid shows the anticipated acid-acid homodimer along with discrete hydrogen bonds between the acid carbonyl and the phenolic moiety. The robust acid-acid homodimer appears to be very stable and is retained in the structures of two co-crystals (SA[middle dot]NIA and SA[middle dot]PYC). In these cases, co-crystallization occurs via intermolecular phenol O-H[three dots, centered]Naromatic hydrogen bonds between the co-formers. In the SA[middle dot]PTU[middle dot]2MeCN co-crystal the acid-acid homodimer gives way to the anticipated acid-amide heterodimer, with the phenolic moiety of SA hydrogen-bonded to acetonitrile. Attempts at obtaining the desolvated co-crystal led to lattice breakdown, thus highlighting the importance of acetonitrile in the formation of the co-crystal. Among the co-crystals examined, SA[middle dot]INC (5 weeks), SA[middle dot]NIA (8 weeks) and SA[middle dot]PYC (5 weeks) were found to be stable under accelerated humidity conditions (40 [degree]C, 75% RH), whereas SA[middle dot]PTU[middle dot]2MeCN decomposed after one week into individual components due to solvent loss

Sensitive liquid chromatography-tandem mass spectrometry method for the determination of pantoprazole sodium in human urine

A sensitive and selective liquid chromatographic tandem mass spectrometric (LC-MS-MS) method was developed to determine pantoprazole sodium (PNT) in human urine. After solid-phase extraction with SPE cartridge, the urine sample was analysed on a C-18 column (symmetry 3.5 mu m; 75 mm x 4.6 mm i.d) interfaced with a triple quadrupole tandem mass spectrometer. Positive electrospray ionization was employed as the ionization source. The mobile phase consisted of acetonitrile-water (90:10, v/v). The method was linear over a concentration range of 1-100 ng mL(-1). The lower limit of quantitation was 1 ng mL(-1). The intra-day and inter-day relative standard deviation across three validation runs over the entire concentration range was < 10.5%. The accuracy determined at three concentrations (8.0, 50.0 and 85.0 ng mL(-1) PNT) was within +/- 1.25% in terms of relative errors. (c) 2010 King Saud University. Production and hosting by Elsevier B.V. All rights reserved

Potential Mechanisms for Cancer Resistance in Elephants and Comparative Cellular Response to DNA Damage in Humans

Importance: Evolutionary medicine may provide insights into human physiology and pathophysiology, including tumor biology. Objective: To identify mechanisms for cancer resistance in elephants and compare cellular response to DNA damage among elephants, healthy human controls, and cancer-prone patients with Li-Fraumeni syndrome (LFS). Design, Setting, and Participants: A comprehensive survey of necropsy data was performed across 36 mammalian species to validate cancer resistance in large and long-lived organisms, including elephants (n = 644). The African and Asian elephant genomes were analyzed for potential mechanisms of cancer resistance. Peripheral blood lymphocytes from elephants, healthy human controls, and patients with LFS were tested in vitro in the laboratory for DNA damage response. The study included African and Asian elephants (n = 8), patients with LFS (n = 10), and age-matched human controls (n = 11). Human samples were collected at the University of Utah between June 2014 and July 2015. Exposures: Ionizing radiation and doxorubicin. Main Outcomes and Measures: Cancer mortality across species was calculated and compared by body size and life span. The elephant genome was investigated for alterations in cancer-related genes. DNA repair and apoptosis were compared in elephant vs human peripheral blood lymphocytes. Results: Across mammals, cancer mortality did not increase with body size and/or maximum life span (eg, for rock hyrax, 1% [95% CI, 0%-5%]; African wild dog, 8% [95% CI, 0%-16%]; lion, 2% [95% CI, 0%-7%]). Despite their large body size and long life span, elephants remain cancer resistant, with an estimated cancer mortality of 4.81% (95% CI, 3.14%-6.49%), compared with humans, who have 11% to 25% cancer mortality. While humans have 1 copy (2 alleles) of TP53, African elephants have at least 20 copies (40 alleles), including 19 retrogenes (38 alleles) with evidence of transcriptional activity measured by reverse transcription polymerase chain reaction. In response to DNA damage, elephant lymphocytes underwent p53-mediated apoptosis at higher rates than human lymphocytes proportional to TP53 status (ionizing radiation exposure: patients with LFS, 2.71% [95% CI, 1.93%-3.48%] vs human controls, 7.17% [95% CI, 5.91%-8.44%] vs elephants, 14.64% [95% CI, 10.91%-18.37%]; P \u3c .001; doxorubicin exposure: human controls, 8.10% [95% CI, 6.55%-9.66%] vs elephants, 24.77% [95% CI, 23.0%-26.53%]; P \u3c .001). Conclusions and Relevance: Compared with other mammalian species, elephants appeared to have a lower-than-expected rate of cancer, potentially related to multiple copies of TP53. Compared with human cells, elephant cells demonstrated increased apoptotic response following DNA damage. These findings, if replicated, could represent an evolutionary-based approach for understanding mechanisms related to cancer suppression