On Closest Pair in Euclidean Metric: Monochromatic is as Hard as Bichromatic

Given a set of n points in R^d, the (monochromatic) Closest Pair problem asks to find a pair of distinct points in the set that are closest in the l_p-metric. Closest Pair is a fundamental problem in Computational Geometry and understanding its fine-grained complexity in the Euclidean metric when d=omega(log n) was raised as an open question in recent works (Abboud-Rubinstein-Williams [FOCS\u2717], Williams [SODA\u2718], David-Karthik-Laekhanukit [SoCG\u2718]). In this paper, we show that for every p in R_{>= 1} cup {0}, under the Strong Exponential Time Hypothesis (SETH), for every epsilon>0, the following holds: - No algorithm running in time O(n^{2-epsilon}) can solve the Closest Pair problem in d=(log n)^{Omega_{epsilon}(1)} dimensions in the l_p-metric. - There exists delta = delta(epsilon)>0 and c = c(epsilon)>= 1 such that no algorithm running in time O(n^{1.5-epsilon}) can approximate Closest Pair problem to a factor of (1+delta) in d >= c log n dimensions in the l_p-metric. In particular, our first result is shown by establishing the computational equivalence of the bichromatic Closest Pair problem and the (monochromatic) Closest Pair problem (up to n^{epsilon} factor in the running time) for d=(log n)^{Omega_epsilon(1)} dimensions. Additionally, under SETH, we rule out nearly-polynomial factor approximation algorithms running in subquadratic time for the (monochromatic) Maximum Inner Product problem where we are given a set of n points in n^{o(1)}-dimensional Euclidean space and are required to find a pair of distinct points in the set that maximize the inner product. At the heart of all our proofs is the construction of a dense bipartite graph with low contact dimension, i.e., we construct a balanced bipartite graph on n vertices with n^{2-epsilon} edges whose vertices can be realized as points in a (log n)^{Omega_epsilon(1)}-dimensional Euclidean space such that every pair of vertices which have an edge in the graph are at distance exactly 1 and every other pair of vertices are at distance greater than 1. This graph construction is inspired by the construction of locally dense codes introduced by Dumer-Miccancio-Sudan [IEEE Trans. Inf. Theory\u2703]

Parameterized Intractability of Even Set and Shortest Vector Problem from Gap-ETH

The k-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over F_2, which can be stated as follows: given a generator matrix A and an integer k, determine whether the code generated by A has distance at most k. Here, k is the parameter of the problem. The question of whether k-Even Set is fixed parameter tractable (FPT) has been repeatedly raised in literature and has earned its place in Downey and Fellows\u27 book (2013) as one of the "most infamous" open problems in the field of Parameterized Complexity. In this work, we show that k-Even Set does not admit FPT algorithms under the (randomized) Gap Exponential Time Hypothesis (Gap-ETH) [Dinur\u2716, Manurangsi-Raghavendra\u2716]. In fact, our result rules out not only exact FPT algorithms, but also any constant factor FPT approximation algorithms for the problem. Furthermore, our result holds even under the following weaker assumption, which is also known as the Parameterized Inapproximability Hypothesis (PIH) [Lokshtanov et al.\u2717]: no (randomized) FPT algorithm can distinguish a satisfiable 2CSP instance from one which is only 0.99-satisfiable (where the parameter is the number of variables). We also consider the parameterized k-Shortest Vector Problem (SVP), in which we are given a lattice whose basis vectors are integral and an integer k, and the goal is to determine whether the norm of the shortest vector (in the l_p norm for some fixed p) is at most k. Similar to k-Even Set, this problem is also a long-standing open problem in the field of Parameterized Complexity. We show that, for any p > 1, k-SVP is hard to approximate (in FPT time) to some constant factor, assuming PIH. Furthermore, for the case of p = 2, the inapproximability factor can be amplified to any constant

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions

AUDIO CLASSIFICATION IN SPEECH AND MUSIC: A COMPARISON OF DIFFERENT APPROACHES

This paper presents a comparison between different techniques for audio classification into homogeneous segments of speech and music. The first method is based on Zero Crossing Rate and Bayesian Classification (ZB), and it is very simple from a computational point of view. The second approach uses a Multi Layer Perceptron network (MLP) and requires therefore more computations. The performance of the proposed algorithms has been evaluated in terms of misclassification errors and precision in music-speech change detection. Both the proposed algorithms give good results, even if the MLP shows the best performance

Finding the proverbial needle: Non-targeted screening of synthetic opioids in equine plasma.

Synthetic opioids are a class of compounds that are of particular concern due to their high potency and potential health impacts. With the relentless emergence of new synthetic opioid derivatives, non-targeted screening strategies are required that do not rely on the use of library spectra or reference materials. In this study, product ion searching, and Kendrick mass defect analysis were investigated for non-targeted screening of synthetic opioids. The estimated screening cut-offs for these techniques ranged between 0.05 and 0.1 ng/mL. These techniques were designed to not be reliant on a particular vendor's software, meaning that they can be applied to existing drug screening protocols, without requiring the development and validation of new analytical procedures. The efficacy of the developed techniques was tested through blind trials, with spiked samples inserted amongst authentic plasma samples, which demonstrated the usefulness of these methods for high-throughput screening. The use of a non-targeted screening workflow that contains complementary techniques can increase the likelihood of detecting compounds of interest within a sample, as well as the confidence in detections that are made

Medico-legal considerations in a case of splenic injury that occurred during colonoscopy

Colonoscopy has became the gold standard diagnostic and therapeutic treatment for rectum and colon diseases. The splenic injury is a rare complication of colonoscopy and relatively few cases (less than 70) have been reported in the literature so far. Here we present a case of splenic rupture identified in a 80 year-old man few hours after an apparently uneventful colonoscopy. Acknowledging a causal relationship between the lesion and the diagnostic procedures, we discuss the possible medico-legal implications with regard to professional liability considering the exceptional nature of such an event and the stance recently taken by the Italian law

Brewers' spent grain as substrates for production of cellulolytic and hemicellulolytic enzymes by different Aspergillus species

Brewers' spent grain (BSG) is the major by-product of the brewing industry, representing around 85% of the total by-products generated. It is a lignocellulosic material containing about 38% cellulose, 29% hemicellulose, chiefly arabinoxylans, and 13% lignin. The production of cellulolytic and hemicellulolytic enzymes using this material as substrate represent an eco-friendly strategy for the lignocellulosic biomass hydrolysis, generating fermentable sugars that can be converted into high- added value products, such as bioethanol, lactic acid, xylitol and others. Thus, this work aimed to evaluate the potential of cellulolytic and hemicellulolytic enzymes production by some Aspergillus species cultivated in BSG. Fungi were grown in minimum media, pH 6.5, with 1% BSG and inoculum was done with 107spores/mL, cultivated at 30°C, 120 rpm, for 5 days. Every 24 hours 2 mL of the samples were collected. The enzymatic activity was performed after the incubation of the crude extract with 1% Linear arabinan, Xylan from beechwood, Xyloglucan, Locust bean gum and CMC, at 50°C for 60 minutes and the reducing sugars were determined using dinitrosalicylic acid (DNS). Synthetic substrates (2 mM of PNP--L-arabinofuranoside, PNP--D-xylopyranoside, PNP--Dglucopyranoside and PNP--D-cellobioside) were also used at the same conditions. The extract from A. niveus showed the best arabinanase (0.284 U/mL) and -glucosidase (0.126 U/mL) activities after 48 and 96 hours of cultivation, respectively. On the other hand, the extract from A. brasiliensis presented the best activities of -L-arabinofuranosidase (0.129 U/mL), -xylosidase (0.265 U/mL) and xylanase (2.15 U/mL) when cultivated for 48 hours. After 72 hours, this fungus also showed the best activities for xyloglucanase (1.06 U/mL), mannanase (0.617 U/mL) and endoglucanase (0.254 U/mL). The extract produced by A. flavus presented the best cellobiohydrolase activity with 0.113 U/mL after 120 hours of cultivation. It is important to mention that A. awamori, A. clavatus and A. terreus also showed good levels of different enzymes produced but they were not the best producers. These data suggest the great potential of different cellulolytic and hemicellulolytic enzymes production using BSG as substrate, which represents an eco-friendly destination for the residues and can generate high-added value products with great biotechnological application.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Institutos Nacionais de Ciência e Tecnologia (INCT)Fundação para a Ciência e a Tecnologia (FCT)info:eu-repo/semantics/publishedVersio

Production of an enzymatic cocktail by Aspergillus awamori grown on corn straw with stirred tank bioreactor

Increased agroindustrial activity has led to the accumulation of large amounts of lignocellulosic material (LCM). LCM is nature's most abundant source of renewable carbon, representing a valuable industrial substrate with potential for many applications. Thus, the objective of this work was to screen for different holocellulases and to analyze the production of an Aspergillus awamori enzyme cocktail grown in corn straw (CS) using a stirred tank bioreactor. Screening was performed with A. clavatus, A. flavus, A. terreus, A. niveus, A. awamori and A. brasiliensis cultivated in minimal medium (MM), with 1% CS at 30 ºC or 37 ºC (for A. niveus), 120 rpm, for 5 days. Xylanase (XYN) and endoglucanase (EG) activities were evaluated by formation of reducing sugars using dinitrosalicylic acid (DNS). Cellobiohydrolase (CBH), -glucosidase (BGL) and -xylosidase (BXL) were determined by cleavage of PNP--D-cellobioside, PNP--D-glucopyranoside and PNP--D- xylopyranoside, respectively. After screening, a pre-inoculum was prepared with the best enzyme producer using a 500 mL MM flask and incubated at 30 °C, 120 rpm for 48 hours. The increase of enzyme production was performed in a Benchtop BioFlo 310 bioreactor, with 4.5 L of MM and 1% of CS, and was then inoculated the best enzyme producer. Cultivation was performed at 30 °C, pH 6.5, 275 rpm, air flow 2 v.v.m., for 5 days. During the screening, all fungi presented EG, CBH, BGL, XYN and BXL activities. However, A. awamori was chosen to continue the experiments because of its BXL activity which was 12.6 times higher than that produced by A. niveus. At the scale-up stage, XYN production (47.80 U/ mL) increased 4.1-fold compared to flask activity (11.52 U/mL). BXL also showed 1.6-times higher activity, as well as EG, CBH and BGL, which improved 2.3, 3.3 and 1.2 times their activities, respectively. It was concluded that the staggering of cocktail production improved the enzymatic activities and that corn straw is an excellent source of induction. Furthermore, this cocktail has the potential to be applied in the hydrolysis of different LCM due to the range of holocellulases present.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Institutos Nacionais de Ciência e Tecnologia (INCT)Fundação para a Ciência e a Tecnologia (FCT)info:eu-repo/semantics/publishedVersio