We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is constructed. We prove that each categorical group gives rise to c-groups and to a c-crossed module, which is a connected, special and strict c-crossed module in the sense defined by us. The results obtained here will be applied in the proof of an equivalence of the categories of categorical groups and connected, special and strict c-crossed modules.

We study the bi-commutators $[T_1, [b, T_2]]$ of pointwise multiplication and Calder'on-Zygmund operators, and characterize their $L^{p_1}L^{p_2} o L^{q_1}L^{q_2}$ boundedness for several off-diagonal regimes of the mixed-norm integrability exponents $(p_1,p_2) eq(q_1,q_2)$. The strategy is based on a bi-parameter version of the recent approximate weak factorization method.

The main goal of this paper is to achieve a parametrization of the solution set of the truncated matricial Hausdorff moment problem in the non-degenerate and degenerate situation. We treat the even and the odd cases simultaneously. Our approach is based on Schur analysis methods. More precisely, we use two interrelated versions of Schur-type algorithms, namely an algebraic one and a function-theoretic one. The algebraic version, worked out in our former paper arXiv:1908.05115, is an algorithm which is applied to finite or infinite sequences of complex matrices. The construction and discussion of the function-theoretic version is a central theme of this paper. This leads us to a complete description via Stieltjes transform of the solution set of the moment problem under consideration. Furthermore, we discuss special solutions in detail.

In this paper, we give a criterion of the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph: the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ is Gorenstein if and only if (1) sizes of maximal cliques are constant (say $n$) and (2) (a) $n=1$, (b) $n=2$ and there is no odd cycle without chord and length at least 7 or (c) $ngeq 3$ and there is no odd cycle without chord and length at least 5.

We investigate the evolution in time of the position of a fixed number inthe insertion tableau when the Robinson-Schensted-Knuth algorithm is applied to asequence of random numbers. When the length of the sequence tends to infinity, a typical trajectory after scaling converges uniformly in probability to some deterministiccurve.

We equip the type A diagrammatic Hecke category with a special derivation, so that after specialization to characteristic p it becomes a p-dg category. We prove that the defining relations of the Hecke algebra are satisfied in the p-dg Grothendieck group. We conjecture that the $p$-dg Grothendieck group is isomorphic to the Iwahori-Hecke algebra, equipping it with a basis which may differ from both the Kazhdan-Lusztig basis and the p-canonical basis. More precise conjectures will be found in the sequel.

Here are some other results contained in this paper. We provide an incomplete proof of the classification of all degree +2 derivations on the diagrammatic Hecke category, and a complete proof of the classification of those derivations for which the defining relations of the Hecke algebra are satisfied in the p-dg Grothendieck group. In particular, our special derivation is unique up to duality and equivalence. We prove that no such derivation exists in simply-laced types outside of finite and affine type A. We also examine a particular Bott-Samelson bimodule in type A_7, which is indecomposable in characteristic 2 but decomposable in all other characteristics. We prove that this Bott-Samelson bimodule admits no nontrivial fantastic filtrations in any characteristic, which is the analogue in the p-dg setting of being indecomposable.

Quantum computing has evolved quickly in recent years and is showing significant benefits in a variety of fields. Malware analysis is one of those fields that could also take advantage of quantum computing. The combination of software used to locate the most frequent hashes and $n$-grams between benign and malicious software (KiloGram) and a quantum search algorithm could be beneficial, by loading the table of hashes and $n$-grams into a quantum computer, and thereby speeding up the process of mapping $n$-grams to their hashes. The first phase will be to use KiloGram to find the top-$k$ hashes and $n$-grams for a large malware corpus. From here, the resulting hash table is then loaded into a quantum machine. A quantum search algorithm is then used search among every permutation of the entangled key and value pairs to find the desired hash value. This prevents one from having to re-compute hashes for a set of $n$-grams, which can take on average $O(MN)$ time, whereas the quantum algorithm could take $O(sqrt{N})$ in the number of table lookups to find the desired hash values.

Recent single image unsupervised representation learning techniques show remarkable success on a variety of tasks. The basic principle in these works is instance discrimination: learning to differentiate between two augmented versions of the same image and a large batch of unrelated images. Networks learn to ignore the augmentation noise and extract semantically meaningful representations. Prior work uses artificial data augmentation techniques such as cropping, and color jitter which can only affect the image in superficial ways and are not aligned with how objects actually change e.g. occlusion, deformation, viewpoint change. In this paper, we argue that videos offer this natural augmentation for free. Videos can provide entirely new views of objects, show deformation, and even connect semantically similar but visually distinct concepts. We propose Video Noise Contrastive Estimation, a method for using unlabeled video to learn strong, transferable single image representations. We demonstrate improvements over recent unsupervised single image techniques, as well as over fully supervised ImageNet pretraining, across a variety of temporal and non-temporal tasks. Code and the Random Related Video Views dataset are available at https://www.github.com/danielgordon10/vince

This paper considers the multi-group multicast beamforming optimization problem, for which the optimal solution has been unknown due to the non-convex and NP-hard nature of the problem. By utilizing the successive convex approximation numerical method and Lagrangian duality, we obtain the optimal multicast beamforming solution structure for both the quality-of-service (QoS) problem and the max-min fair (MMF) problem. The optimal structure brings valuable insights into multicast beamforming: We show that the notion of uplink-downlink duality can be generalized to the multicast beamforming problem. The optimal multicast beamformer is a weighted MMSE filter based on a group-channel direction: a generalized version of the optimal downlink multi-user unicast beamformer. We also show that there is an inherent low-dimensional structure in the optimal multicast beamforming solution independent of the number of transmit antennas, leading to efficient numerical algorithm design, especially for systems with large antenna arrays. We propose efficient algorithms to compute the multicast beamformer based on the optimal beamforming structure. Through asymptotic analysis, we characterize the asymptotic behavior of the multicast beamformers as the number of antennas grows, and in turn, provide simple closed-form approximate multicast beamformers for both the QoS and MMF problems. This approximation offers practical multicast beamforming solutions with a near-optimal performance at very low computational complexity for large-scale antenna systems.

The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical mixing time. In this article, we deal with analog quantum algorithms for mixing. First, we provide an analog quantum algorithm that given a Markov chain, allows us to sample from its stationary distribution in a time that scales as the sum of the square root of the classical mixing time and the square root of the classical hitting time. Our algorithm makes use of the framework of interpolated quantum walks and relies on Hamiltonian evolution in conjunction with von Neumann measurements.

There also exists a different notion for quantum mixing: the problem of sampling from the limiting distribution of quantum walks, defined in a time-averaged sense. In this scenario, the quantum mixing time is defined as the time required to sample from a distribution that is close to this limiting distribution. Recently we provided an upper bound on the quantum mixing time for Erd"os-Renyi random graphs [Phys. Rev. Lett. 124, 050501 (2020)]. Here, we also extend and expand upon our findings therein. Namely, we provide an intuitive understanding of the state-of-the-art random matrix theory tools used to derive our results. In particular, for our analysis we require information about macroscopic, mesoscopic and microscopic statistics of eigenvalues of random matrices which we highlight here. Furthermore, we provide numerical simulations that corroborate our analytical findings and extend this notion of mixing from simple graphs to any ergodic, reversible, Markov chain.

The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) scheme is used extensively in astrophysics for data collection and analysis on the sphere. The scheme was originally designed for studying the Cosmic Microwave Background (CMB) radiation, which represents the first light to travel during the early stages of the universe's development and gives the strongest evidence for the Big Bang theory to date. Refined analysis of the CMB angular power spectrum can lead to revolutionary developments in understanding the nature of dark matter and dark energy. In this paper, we present a new method for performing spherical harmonic analysis for HEALPix data, which is a central component to computing and analyzing the angular power spectrum of the massive CMB data sets. The method uses a novel combination of a non-uniform fast Fourier transform, the double Fourier sphere method, and Slevinsky's fast spherical harmonic transform (Slevinsky, 2019). For a HEALPix grid with $N$ pixels (points), the computational complexity of the method is $mathcal{O}(Nlog^2 N)$, with an initial set-up cost of $mathcal{O}(N^{3/2}log N)$. This compares favorably with $mathcal{O}(N^{3/2})$ runtime complexity of the current methods available in the HEALPix software when multiple maps need to be analyzed at the same time. Using numerical experiments, we demonstrate that the new method also appears to provide better accuracy over the entire angular power spectrum of synthetic data when compared to the current methods, with a convergence rate at least two times higher.

We investigate sparse matrix bipartitioning -- a problem where we minimize the communication volume in parallel sparse matrix-vector multiplication. We prove, by reduction from graph bisection, that this problem is $mathcal{NP}$-complete in the case where each side of the bipartitioning must contain a linear fraction of the nonzeros.

We present an improved exact branch-and-bound algorithm which finds the minimum communication volume for a given matrix and maximum allowed imbalance. The algorithm is based on a maximum-flow bound and a packing bound, which extend previous matching and packing bounds.

We implemented the algorithm in a new program called MP (Matrix Partitioner), which solved 839 matrices from the SuiteSparse collection to optimality, each within 24 hours of CPU-time. Furthermore, MP solved the difficult problem of the matrix cage6 in about 3 days. The new program is on average more than ten times faster than the previous program MondriaanOpt.

Benchmark results using the set of 839 optimally solved matrices show that combining the medium-grain/iterative refinement methods of the Mondriaan package with the hypergraph bipartitioner of the PaToH package produces sparse matrix bipartitionings on average within 10% of the optimal solution.

This paper is the first to consider online algorithms to schedule a proportionate flexible flow shop of batching machines (PFFB). The scheduling model is motivated by manufacturing processes of individualized medicaments, which are used in modern medicine to treat some serious illnesses. We provide two different online algorithms, proving also lower bounds for the offline problem to compute their competitive ratios. The first algorithm is an easy-to-implement, general local scheduling heuristic. It is 2-competitive for PFFBs with an arbitrary number of stages and for several natural scheduling objectives. We also show that for total/average flow time, no deterministic algorithm with better competitive ratio exists. For the special case with two stages and the makespan or total completion time objective, we describe an improved algorithm that achieves the best possible competitive ratio $varphi=frac{1+sqrt{5}}{2}$, the golden ratio. All our results also hold for proportionate (non-flexible) flow shops of batching machines (PFB) for which this is also the first paper to study online algorithms.

In this paper, we present three distributed algorithms to solve a class of generalized Nash equilibrium (GNE) seeking problems in strongly monotone games. The first one (SD-GENO) is based on synchronous updates of the agents, while the second and the third (AD-GEED and AD-GENO) represent asynchronous solutions that are robust to communication delays. AD-GENO can be seen as a refinement of AD-GEED, since it only requires node auxiliary variables, enhancing the scalability of the algorithm. Our main contribution is to prove converge to a variational GNE of the game via an operator-theoretic approach. Finally, we apply the algorithms to network Cournot games and show how different activation sequences and delays affect convergence. We also compare the proposed algorithms to the only other in the literature (ADAGNES), and observe that AD-GENO outperforms the alternative.

For any finite Galois field extension $mathsf{K}/mathsf{F}$, with Galois group $G = mathrm{Gal}(mathsf{K}/mathsf{F})$, there exists an element $alpha in mathsf{K}$ whose orbit $Gcdotalpha$ forms an $mathsf{F}$-basis of $mathsf{K}$. Such an $alpha$ is called a normal element and $Gcdotalpha$ is a normal basis. We introduce a probabilistic algorithm for testing whether a given $alpha in mathsf{K}$ is normal, when $G$ is either a finite abelian or a metacyclic group. The algorithm is based on the fact that deciding whether $alpha$ is normal can be reduced to deciding whether $sum_{g in G} g(alpha)g in mathsf{K}[G]$ is invertible; it requires a slightly subquadratic number of operations. Once we know that $alpha$ is normal, we show how to perform conversions between the working basis of $mathsf{K}/mathsf{F}$ and the normal basis with the same asymptotic cost.

One of the main open problems in the qualitative theory of real planar differential systems is the study of limit cycles. In this article, we present an algorithmic approach for detecting how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems via the averaging method. We propose four symbolic algorithms to implement the averaging method. The first algorithm is based on the change of polar coordinates that allows one to transform a considered differential system to the normal form of averaging. The second algorithm is used to derive the solutions of certain differential systems associated to the unperturbed term of the normal of averaging. The third algorithm exploits the partial Bell polynomials and allows one to compute the integral formula of the averaged functions at any order. The last algorithm is based on the aforementioned algorithms and determines the exact expressions of the averaged functions for the considered differential systems. The implementation of our algorithms is discussed and evaluated using several examples. The experimental results have extended the existing relevant results for certain classes of differential systems.

Consider the following prediction problem. Assume that there is a block box that produces bits according to some unknown computable distribution on the binary tree. We know first $n$ bits $x_1 x_2 ldots x_n$. We want to know the probability of the event that that the next bit is equal to $1$. Solomonoff suggested to use universal semimeasure $m$ for solving this task. He proved that for every computable distribution $P$ and for every $b in {0,1}$ the following holds: $$sum_{n=1}^{infty}sum_{x: l(x)=n} P(x) (P(b | x) - m(b | x))^2 < infty .$$ However, Solomonoff's method has a negative aspect: Hutter and Muchnik proved that there are an universal semimeasure $m$, computable distribution $P$ and a random (in Martin-L{"o}f sense) sequence $x_1 x_2ldots$ such that $lim_{n o infty} P(x_{n+1} | x_1ldots x_n) - m(x_{n+1} | x_1ldots x_n) rightarrow 0$. We suggest a new way for prediction. For every finite string $x$ we predict the new bit according to the best (in some sence) distribution for $x$. We prove the similar result as Solomonoff theorem for our way of prediction. Also we show that our method of prediction has no that negative aspect as Solomonoff's method.

Most currently available schemes for performance based ranking of Universities or Research organizations, such as, Quacarelli Symonds (QS), Times Higher Education (THE), Shanghai University based All Research of World Universities (ARWU) use a variety of criteria that include productivity, citations, awards, reputation, etc., while Leiden and Scimago use only bibliometric indicators. The research performance evaluation in the aforesaid cases is based on bibliometric data from Web of Science or Scopus, which are commercially available priced databases. The coverage includes peer reviewed journals and conference proceedings. Google Scholar (GS) on the other hand, provides a free and open alternative to obtaining citations of papers available on the net, (though it is not clear exactly which journals are covered.) Citations are collected automatically from the net and also added to self created individual author profiles under Google Scholar Citations (GSC). This data was used by Webometrics Lab, Spain to create a ranked list of 4000+ institutions in 2016, based on citations from only the top 10 individual GSC profiles in each organization. (GSC excludes the top paper for reasons explained in the text; the simple selection procedure makes the ranked list size-independent as claimed by the Cybermetrics Lab). Using this data (Transparent Ranking TR, 2016), we find the regional and country wise distribution of GS-TR Citations. The size independent ranked list is subdivided into deciles of 400 institutions each and the number of institutions and citations of each country obtained for each decile. We test for correlation between institutional ranks between GS TR and the other ranking schemes for the top 20 institutions.

Over the years, performance evaluation has become essential in computer vision, enabling tangible progress in many sub-fields. While talking-head video generation has become an emerging research topic, existing evaluations on this topic present many limitations. For example, most approaches use human subjects (e.g., via Amazon MTurk) to evaluate their research claims directly. This subjective evaluation is cumbersome, unreproducible, and may impend the evolution of new research. In this work, we present a carefully-designed benchmark for evaluating talking-head video generation with standardized dataset pre-processing strategies. As for evaluation, we either propose new metrics or select the most appropriate ones to evaluate results in what we consider as desired properties for a good talking-head video, namely, identity preserving, lip synchronization, high video quality, and natural-spontaneous motion. By conducting a thoughtful analysis across several state-of-the-art talking-head generation approaches, we aim to uncover the merits and drawbacks of current methods and point out promising directions for future work. All the evaluation code is available at: https://github.com/lelechen63/talking-head-generation-survey.

Most optimization-based community detection approaches formulate the problem in a single or bi-objective framework. In this paper, we propose two variants of a three-objective formulation using a customized non-dominated sorting genetic algorithm III (NSGA-III) to find community structures in a network. In the first variant, named NSGA-III-KRM, we considered Kernel k means, Ratio cut, and Modularity, as the three objectives, whereas the second variant, named NSGA-III-CCM, considers Community score, Community fitness and Modularity, as three objective functions. Experiments are conducted on four benchmark network datasets. Comparison with state-of-the-art approaches along with decomposition-based multi-objective evolutionary algorithm variants (MOEA/D-KRM and MOEA/D-CCM) indicates that the proposed variants yield comparable or better results. This is particularly significant because the addition of the third objective does not worsen the results of the other two objectives. We also propose a simple method to rank the Pareto solutions so obtained by proposing a new measure, namely the ratio of the hyper-volume and inverted generational distance (IGD). The higher the ratio, the better is the Pareto set. This strategy is particularly useful in the absence of empirical attainment function in the multi-objective framework, where the number of objectives is more than two.

In this technical report we give an elementary introduction to Quantum Computing for non-physicists. In this introduction we describe in detail some of the foundational Quantum Algorithms including: the Deutsch-Jozsa Algorithm, Shor's Algorithm, Grocer Search, and Quantum Counting Algorithm and briefly the Harrow-Lloyd Algorithm. Additionally we give an introduction to Solomonoff Induction, a theoretically optimal method for prediction. We then attempt to use Quantum computing to find better algorithms for the approximation of Solomonoff Induction. This is done by using techniques from other Quantum computing algorithms to achieve a speedup in computing the speed prior, which is an approximation of Solomonoff's prior, a key part of Solomonoff Induction. The major limiting factors are that the probabilities being computed are often so small that without a sufficient (often large) amount of trials, the error may be larger than the result. If a substantial speedup in the computation of an approximation of Solomonoff Induction can be achieved through quantum computing, then this can be applied to the field of intelligent agents as a key part of an approximation of the agent AIXI.

Linkage Tree Genetic Algorithm (LTGA) is an effective Evolutionary Algorithm (EA) to solve complex problems using the linkage information between problem variables. LTGA performs well in various kinds of single-task optimization and yields promising results in comparison with the canonical genetic algorithm. However, LTGA is an unsuitable method for dealing with multi-task optimization problems. On the other hand, Multifactorial Optimization (MFO) can simultaneously solve independent optimization problems, which are encoded in a unified representation to take advantage of the process of knowledge transfer. In this paper, we introduce Multifactorial Linkage Tree Genetic Algorithm (MF-LTGA) by combining the main features of both LTGA and MFO. MF-LTGA is able to tackle multiple optimization tasks at the same time, each task learns the dependency between problem variables from the shared representation. This knowledge serves to determine the high-quality partial solutions for supporting other tasks in exploring the search space. Moreover, MF-LTGA speeds up convergence because of knowledge transfer of relevant problems. We demonstrate the effectiveness of the proposed algorithm on two benchmark problems: Clustered Shortest-Path Tree Problem and Deceptive Trap Function. In comparison to LTGA and existing methods, MF-LTGA outperforms in quality of the solution or in computation time.

We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality !L*, which has a limited edition of the contraction and permutation rules. The categorical part of the semantics is a monoidal biclosed category with a coalgebra modality, very similar to the structure of a Differential Category. We instantiate this category to finite dimensional vector spaces and linear maps via "quantisation" functors and work with three concrete interpretations of the coalgebra modality. We apply the model to construct categorical and concrete semantic interpretations for the motivating example of !L*: the derivation of a phrase with a parasitic gap. The effectiveness of the concrete interpretations are evaluated via a disambiguation task, on an extension of a sentence disambiguation dataset to parasitic gap phrase one, using BERT, Word2Vec, and FastText vectors and Relational tensors.

Dozens of people find your business when looking for a type of product but aren’t sure which product fits their needs best. With a well-designed and organized category page, you’ll help people browse products easier and find what they want. To help you get inspired, let’s take a look at some excellent category page design […]

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If you’re looking to grow your business online, it’s time to start setting up different types of website conversions to help your company succeed. Whether you’re looking to earn more email subscribers or sell more products, you can set conversion goals that grow your business. On this page, we’ll discuss what a conversion goal is, […]

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Summary

One feature that Go does not offer that is really useful in visitor patterns is overriding methods. The basic idea is to write a concrete class that contains all the VisitX methods with empty implementations, and a subclass can choose to only override the methods it cares about, ignoring the rest.

We'll see an example of how to implement this pattern in idiomatic Go code.

See the Code - See it Full Page - See Details

This Pen uses: HTML, CSS, JavaScript, and

See the Code - See it Full Page - See Details

After seeing the amazing [pen](https://codepen.io/oliviale/full/GRpvNBa) from [@Olivia Ng](https://codepen.io/oliviale/pen/GRpvNBa) this is my attempt on the google meets interface. You can "send me" messages in the chat tab. Warning: You won't actually be sending me any messages.

This Pen uses: Pug, SCSS, JavaScript, and

With a relatively successful 2019, I am hitting the ground running into 2020. This is the first year in a long time where I feel like I am at a good starting point. One of the big realizations from the past year…

We could blame the enormous — and justifiable — success of the Lego flicks for the existence of Playmobil: The Movie, but that would be unfair to all the shameless knockoffs and cinematic coattail riders.…

[IMAGE-1] Harrison Ford has gone full Grizzly Adams and Buck the canine hero is fully CGI, 100-percent digital, not a scrap of real fur or dog farts about him. There is so much about this new umpteenth film version of Jack London's classic novel The Call of the Wild that is ready-made for meme-iriffic snarking.…

When it comes to the music scene in the midst of the coronavirus pandemic, the math is pretty simple: No shows equals no revenue.…

This is normally the time of year when we're up to our eyeballs in concert announcements, but in these topsy-turvy times, we're instead having to write about all the concerts being canceled due to COVID-19. It's a real bummer.…

Perhaps you've heard people banging on pans to support health care workers, or howling into the abyss just to let other humans know they were alive. We've gone to some extreme measures to keep ourselves entertained since much of the country went on lockdown to combat COVID-19, and here's another one that can get you out of the house while remaining safely social-distanced and supporting local artists at the same time.…

Gonzaga Athletic Director Mike Roth took to the Zoom online meeting app Wednesday for a lengthy chat with members of the school community, fans and media to answer questions about college sports in the era of COVID-19. Like so many things regarding the coronavirus, there are a lot of hopes for a rapid return to normalcy — all of them couched in the reality that none of us really know how the pandemic is going to affect our lives three months from now, or six months down the line.…

THE SHOW WILL GO ON…

Virtually every musician starts out trying to copy their heroes.…

In times of trouble, escaping into the art that calms you is key to keeping your sanity.…

By Patricia Cohen and Tiffany Hsu The New York Times Company…

Designology Interiors' Deanna Goguen has three bathrooms in her South Hill-area home, each with its own personality.…

[IMAGE-1] It isn't often that you see a local band selling out most of their gigs, but Indian Goat does. The duo of Garrett Zanol and Travis Tveit formed a few years ago and almost immediately struck a chord with Spokane audiences: Their live shows are usually raucous, sweaty, beer-soaked affairs, with rooms crammed full of people rocking out in unison.…

For people who love playing, a day on the worst possible golf course is better than any day not swinging the clubs.…

Erin Haskell Gourde isn't afraid to mix it up a little.…

ProPublica’s health reporter Caroline Chen explains what the conversation around asymptomatic coronavirus carriers is missing, and what we need to understand if we’re going to beat this nefarious virus together. By Caroline Chen, ProPublica In the early days of the coronavirus outbreak in the U.S., around the last week of February, I joked to a colleague that maybe now, finally, people would learn how to wash their hands properly.…

By Michael D. Shear and Sarah Mervosh WASHINGTON — President Donald Trump on Friday openly encouraged right-wing protests of social distancing restrictions in states with stay-at-home orders, a day after announcing guidelines for how the nation’s governors should carry out an orderly reopening of their communities on their own timetables.…

Yesterday, Spokane Mayor Nadine Woodward and other local leaders urged Gov. Jay Inslee to allow Spokane County to open on a different schedule than the rest of the state.  Inslee, however, wouldn't budge.…

Last week, the New York Times dropped a terrifying story: Asian Giant Hornets, or "murder hornets" as more J. Jonah Jameson-esque researchers like to call them, have been identified in Western Washington. These insects can grow up to 2 inches long, can rip the heads off an entire hive of honeybees in a matter of hours, and have dagger-like stingers that pierce beekeeper suits to deliver a sting that sears like molten acid.…

The invention concerns a new process for the preparation of crystalline form of agomelatine from a solution of agomelatine in a solvent, characterized in that the agomelatine is crystallized by instantaneous precipitation from said solution, at a temperature equal to or below −10° C.

The invention relates to a process for the preparation of oligonucleotides by the following steps: reaction of a nucleoside with a phosphine derivative, reaction of the nucleotide derivative thus obtained with a nucleoside bonded to a polymeric carrier, oxidation of the carrier-bound nucleoside-nucleotide thus obtained with formation of phosphotriester groups, blocking of free primary 5'--OH groups, elimination of a protective group from the terminal 5'--OH group, where appropriate single or multiple repetition of the abovementioned steps to introduce further nucleoside phosphate or oligonucleoside phosphate units, and cleavage of the nucleoside-carrier bond and, where appropriate, elimination of all protective groups present in the oligonucleoside phosphates. The phosphine derivative used is a compound of the general formula III ##STR1## in which X and L can react with OH groups of the sugar units in the oligonucleotides, and R3 is a protective group which can be liberated by β-elimination.

The present invention relates to a catalyst composition for oligomerization of ethylene, comprising a chromium compound; a ligand of the general structure R1R2P—N(R3)—P(R4)—N(R5)—H, wherein R1, R2, R3, R4 and R5 are independently selected from halogen, amino, trimethylsilyl, C1-C10-alkyl, aryl and substituted aryl; a modifier containing organic or inorganic halide; and an activator or co-catalyst; and a process for oligomerization utilizing that catalyst.