We study the probabilistic degree over reals of the OR function on \(n\) variables. For an error parameter \(\epsilon\) in (0,1/3), the \(\epsilon\)-error probabilistic degree of any Boolean function ...\(f\) over reals is the smallest non-negative integer \(d\) such that the following holds: there exists a distribution \(D\) of polynomials entirely supported on polynomials of degree at most \(d\) such that for all \(z \in \{0,1\}^n\), we have \(Pr_{P \sim D} P(z) = f(z) \geq 1- \epsilon\). It is known from the works of Tarui ({Theoret. Comput. Sci.} 1993) and Beigel, Reingold, and Spielman ({ Proc. 6th CCC} 1991), that the \(\epsilon\)-error probabilistic degree of the OR function is at most \(O(\log n.\log 1/\epsilon)\). Our first observation is that this can be improved to \(O{\log {{n}\choose{\leq \log 1/\epsilon}}}\), which is better for small values of \(\epsilon\). In all known constructions of probabilistic polynomials for the OR function (including the above improvement), the polynomials \(P\) in the support of the distribution \(D\) have the following special structure:\(P = 1 - (1-L_1).(1-L_2)...(1-L_t)\), where each \(L_i(x_1,..., x_n)\) is a linear form in the variables \(x_1,...,x_n\), i.e., the polynomial \(1-P(x_1,...,x_n)\) is a product of affine forms. We show that the \(\epsilon\)-error probabilistic degree of OR when restricted to polynomials of the above form is \(\Omega ( \log a/\log^2 a )\) where \(a = \log {{n}\choose{\leq \log 1/\epsilon}}\). Thus matching the above upper bound (up to poly-logarithmic factors).
We consider the problem of determining the zero-error list-decoding capacity of the \(q/(q-1)\) channel studied by Elias (1988). The \(q/(q-1)\) channel has input and output alphabet consisting of ...\(q\) symbols, say, \(Q = \{x_1,x_2,\ldots, x_q\}\); when the channel receives an input \(x \in Q\), it outputs a symbol other than \(x\) itself. Let \(n(m,q,\ell)\) be the smallest \(n\) for which there is a code \(C \subseteq Q^n\) of \(m\) elements such that for every list \(w_1, w_2, \ldots, w_{\ell+1}\) of distinct code-words from \(C\), there is a coordinate \(j \in n\) that satisfies \(\{w_1j, w_2j, \ldots, w_{\ell+1}j\} = Q\). We show that for \(\epsilon<1/6\), for all large \(q\) and large enough \(m\), \(n(m,q, \epsilon q\ln{q}) \geq \Omega(\exp{(q^{1-6\epsilon}/8)}\log_2{m})\). The lower bound obtained by Fredman and Koml\'{o}s (1984) for perfect hashing implies that \(n(m,q,q-1) = \exp(\Omega(q)) \log_2 m\); similarly, the lower bound obtained by K\"{o}rner (1986) for nearly-perfect hashing implies that \(n(m,q,q) = \exp(\Omega(q)) \log_2 m\). These results show that the zero-error list-decoding capacity of the \(q/(q-1)\) channel with lists of size at most \(q\) is exponentially small. Extending these bounds, Chakraborty et al. (2006) showed that the capacity remains exponentially small even if the list size is allowed to be as large as \(1.58q\). Our result implies that the zero-error list-decoding capacity of the \(q/(q-1)\) channel with list size \(\epsilon q\) for \(\epsilon<1/6\) is \(\exp{(\Omega(q^{1-6\epsilon}))}\). This resolves the conjecture raised by Chakraborty et al. (2006) about the zero-error list-decoding capcity of the \(q/(q-1)\) channel at larger list sizes.
We highlight the usefulness of city-scale agent-based simulators in studying various non-pharmaceutical interventions to manage an evolving pandemic. We ground our studies in the context of the ...COVID-19 pandemic and demonstrate the power of the simulator via several exploratory case studies in two metropolises, Bengaluru and Mumbai. Such tools become common-place in any city administration's tool kit in our march towards digital health.
Retinal hemodynamics and biomechanics play a significant role in understanding the pathophysiology of several ocular diseases. However, these parameters are significantly affected due to changed ...blood vessel morphology ascribed to pathological conditions, particularly diabetes. In this study, an image-based computational fluid dynamics (CFD) model is applied to examine the effects of changed vascular morphology due to diabetes on blood flow velocity, vorticity, wall shear stress (WSS), and oxygen distribution and compare it with healthy. The 3D patient-specific vascular architecture of diabetic and healthy retina is extracted from Optical Coherence Tomography Angiography (OCTA) images and fundus to extract the capillary level information. Further, Fluid-structure interaction (FSI) simulations have been performed to compare the induced tissue stresses in diabetic and healthy conditions. Results illustrate that most arterioles possess higher velocity, vorticity, WSS, and lesser oxygen concentration than arteries for healthy and diabetic cases. However, an opposite trend is observed for venules and veins. Comparisons show that, on average, the blood flow velocity in the healthy case decreases by 42 % in arteries and 21 % in veins, respectively, compared to diabetic. In addition, the WSS and von Mises stress (VMS) in healthy case decrease by 49 % and 72 % in arteries and by 6 % and 28 % in veins, respectively, when compared with diabetic, making diabetic blood vessels more susceptible to wall rupture and tissue damage. The in-silico results may help predict the possible abnormalities region early, helping the ophthalmologists use these estimates as prognostic tools and tailor patient-specific treatment plans.
•Hemodynamics and biomechanics are investigated in healthy and diabetic retinal blood vessels.•Optical Coherence Tomography Angiography (OCTA) data extracts vascular architecture and tissue anatomy.•High wall shear stress (WSS) and von Mises stress (VMS) in diabetic arteries and veins lead to vascular damage.•Arteries are more prone to tissue injury due to higher WSS and VMS than veins.•The lower oxygen penetration depth in diabetic arteries causes hypoxic regions.
Organochlorine (OC) and organophosphorus (OP) pesticides such as chlorpyrifos (CPF) and endosulfan (ES) have been associated with a plethora of adverse health effects. Helicobacter pylori (H. pylori) ...infection can lead to gastrointestinal diseases by regulating several cellular processes. Thus, the current study focuses on the effect of the co-exposure to pesticides and H. pylori on gastric epithelial cells. We have used the in-silico approach to determine the interactive potential of pesticides and their metabolites with H. pylori-associated proteins. Further, various in-vitro methods depict the potential of ES in enhancing the virulence of H. pylori. Our results showed that ES along with H. pylori affects the mitochondrial dynamics, increases the transcript expression of mitochondrial fission genes, and lowers the mitochondrial membrane potential and biomass. They also promote inflammation and lower oxidative stress as predicted by ROS levels. Furthermore, co-exposure induces the multi-nucleated cells in gastric epithelial cells. In addition, ES along with H. pylori infection follows the extrinsic pathway for apoptotic signaling. H. pylori leads to the NF-κB activation which in turn advances the β-catenin expression. The expression was further enhanced in the co-exposure condition and even more prominent in co-exposure with ES-conditioned media. Thus, our study demonstrated that pesticide and their metabolites enhance the pathogenicity of H. pylori infection.
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•ES metabolites may impact structural and functional integrity of H. pylori protein.•Simultaneous exposure to ES and H. pylori disrupts mitochondrial dynamics.•Co-exposure induces an inflammatory response and reduce ROS in AGS cells.•ES and H. pylori co-exposure induces genomic instability in AGS cells.•Co-exposure of ES and H. pylori-induced NF-κB, and β-catenin activation.
Although intravitreal (IVT) injections provide several advantages in treating posterior segment eye diseases, several associated challenges remain. The current study uses the finite element method ...(FEM) to highlight the effect of IVT needle rotation along the insertion axis on the reaction forces and deformation inside the eye. A comparison of the reaction forces at the eye’s key locations has been made with and without rotation. In addition, a sensitivity analysis of various parameters, such as the needle’s angular speed, insertion location, angle, gauge, shape, and intraocular pressure (IOP), has been carried out to delineate the individual parameter’s effect on reaction forces during rotation. Results demonstrate that twisting the needle significantly reduces the reaction forces at the penetration location and throughout the needle travel length, resulting in quicker penetration. Moreover, ocular biomechanics are influenced by needle insertion location, angle, shape, size, and IOP. The reaction forces incurred by the patient may be reduced by using a bevel needle of the higher gauge when inserted close to the normal of the local scleral surface toward the orra serrata within the Pars Plana region. Results obtained from the current study can deepen the understanding of the twisting needle’s interaction with the ocular tissue.
Background: Out of its various derivatives, low molecular weight (LMW) chitosan is known to have improved solubility and antifungal properties. Nystatin the standard antifungal drug discontinued from ...therapy due to resistant Candida strains emerged. Objectives: This study aims to compare the previously obtained results of the antifungal capacity of LMW chitosan and nystatin against Candida albicans biofilm on Triplex heat-cure denture bases after 7 and 14 days with their antifungal efficacy on Trevalon High-Impact (HI) heat-cure denture bases. Methods: A Trevalon heat-cure with HI, utilizing the typical compression molding process, was employed to create 10 specimens from Polymethyl Methacrylate (PMMA) acrylic resin. All specimens were pretreated with imitation saliva for 72 h to develop biofilm. Two groups of five specimens each were established. On the fourth day after biofilm formation, Group A was immersed in an LMW chitosan solution, whereas Group B was immersed in a nystatin solution. On the 11th day, the specimens were treated again using antifungal suspension, as per the assigned groups, and the complete maturation of the residual biofilm was allowed to occur until the 14th day. Results: The results in nystatin group demonstrated a substantial reduction of 5 times or more in the Colony Forming Units (CFU) of Candida colonies in the biofilm from the 7th to the 14th day. On the other hand, in chitosan group, the CFU of Candida colonies showed an insignificant decrease. When comparing CFU between both groups at one week, a nonsignificant reduction while a significantly lower CFU count was noted at the 14th day in the chitosan group compared to the nystatin group, with a significant P value of 0.002. Conclusion: The current study results suggest the potential for expanding the use of chitosan in denture-wearing patients in the future, contributing to the maintenance of optimal dental and overall health.
Prostate carcinoma is the most common malignancy in males and it commonly manifests with bony metastasis in India, but occasionally visceral metastasis to lungs and liver may also be seen. Metastasis ...to the gastrointestinal tract is very rare. In literature, we could find six cases only. We present here 7 th patient of carcinoma prostate, which metastasized to stomach. He had epigastric pain, which was mistaken initially with analgesic induced acid peptic disease abut later, on endoscopy a gastric nodule was seen. Histopathology and immunohistochemistry of this confirmed it to be metastasis from prostate. This visceral metastasis to stomach usually spreads through lymphatic's rather than by hematogenous route. This case is being presented because of its rare occurrence.
Abstract Background Since we last published our technique of robotic prostatectomy, we have introduced three technical refinements: superveil nerve sparing, bladder drainage with a percutaneous ...suprapubic tube (PST), and limited node dissection of the obturator and internal iliac nodes in preference to the external iliac nodes in selected patients. Objective To describe selection criteria, to explain the three techniques, and to evaluate functional and oncologic results. Design, setting, and participants Single-institution study of 1151 radical prostatectomies performed from 2006 to 2008 by one surgeon. Surgical procedure The superveil nerve-sparing technique spares nerves from the 11-o’clock position to the 1-o’clock position. The bladder is drained with a PST rather than a urethral catheter. For low- or intermediate-risk disease, limited lymphadenectomy concentrates on the internal iliac and obturator nodes, excluding the external iliac lymph nodes. Measurements Erectile function and patient comfort were evaluated using questionnaires administered by a third party. Lymph node yield was quantified by a qualified uropathologist. Results and limitations At 6–18 months after surgery, 94% of men who attempted sexual intercourse were successful with a median Sexual Health Inventory For Men (SHIM) score of 18 out of 25. PST bladder drainage resulted in less patient discomfort; visual analog scores were 2 at 2 days after prostatectomy and 0 at 6 days after prostatectomy. The modified lymphadenectomy harvested few overall nodes, but it increased the yield of positive nodes >13-fold in patients with low-risk stratification (6.7% compared with 0.5%). Conclusion In this single-institution, single-surgeon study, these modifications improved erectile function outcomes, decreased catheter-associated discomfort, and enhanced the detection of positive nodes.
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