A note on the Schur multiplier of a nilpotent Lie algebra

For a nilpotent Lie algebra $L$ of dimension $n$ and dim$(L^2)=m$, we find the upper bound dim$(M(L))\leq {1/2}(n+m-2)(n-m-1)+1$, where $M(L)$ denotes the Schur multiplier of $L$. In case $m=1$ the equality holds if and only if $L\cong H(1)\oplus A$, where $A$ is an abelian Lie algebra of dimension $n-3$ and H(1) is the Heisenberg algebra of dimension 3.Comment: Paper in press in Comm. Algebra with small revision

Exactness of the Original Grover Search Algorithm

It is well-known that when searching one out of four, the original Grover's search algorithm is exact; that is, it succeeds with certainty. It is natural to ask the inverse question: If we are not searching one out of four, is Grover's algorithm definitely not exact? In this article we give a complete answer to this question through some rationality results of trigonometric functions.Comment: 8 pages, 2 figure

Bridging languages through images with deep partial canonical correlation analysis

We present a deep neural network that leverages images to improve bilingual text embeddings. Relying on bilingual image tags and descriptions, our approach conditions text embedding induction on the shared visual information for both languages, producing highly correlated bilingual embeddings. In particular, we propose a novel model based on Partial Canonical Correlation Analysis (PCCA). While the original PCCA finds linear projections of two views in order to maximize their canonical correlation conditioned on a shared third variable, we introduce a non-linear Deep PCCA (DPCCA) model, and develop a new stochastic iterative algorithm for its optimization. We evaluate PCCA and DPCCA on multilingual word similarity and cross-lingual image description retrieval. Our models outperform a large variety of previous methods, despite not having access to any visual signal during test time inference. Our code and data are available at: https://github.com/rotmanguy/DPCCA

Localization during Pursuit Eye Movement

__Abstract__ Humans are very good at acquiring complex skills. More than probably any other species they learn a large array of new capabilities after they are born. Special institutions (e.g. schools, sporting clubs, handwork courses, etc.) have been put into operation to optimize the learning of such skills. It can be very pleasurable to acquire or optimize your skills, as is evident from the popularity of sporting clubs. In sports, precise coordination of different body parts is generally important. You must be somewhere at exactly the right time, for example to catch a ball when playing baseball. In other cases you must bring an object like a ball or a dart in such a condition that after you lose contact with it (and thus control over it) the object will move to some intended position. The timing and positioning requirements in sports can be very demanding (e.g. Regan 1992), but ordinary actions in daily life also require precise co-ordination. For example, when grasping an object that has a width of 10 centimeters while you are walking at a moderate speed (i.e. 5 km/hour), your hand will move past the object in less than one tenth of a second. In order to be successful you not only have to position your hand at the right place but it also has to be there at the right time, which is often a very short period. Knowing "the right place" is also far from easy, because at the moment that the brain sends the movement commands to the muscles, the object of interest is not there yet. So, obviously, some kind of prediction must be made. Eye movements are very important to gather the required information for such a prediction. For example, Land and Fumeaux (1997) argue that the eyes move in ways that optimize the uptake of information that is useful in such diverse activities as playing table tenni

Idiopathic desquamative interstitial pneumonia in a child: a case report.

Desquamative interstitial pneumonia is a rare form of interstitial lung disease in children. Respiratory symptoms appear progressively, are often subtle, and diagnosis is often delayed by a mean of 6 months after onset. High resolution chest computed tomography is the most sensitive imaging technique for demonstrating and identifying interstitial pneumonia. The typical histologic pattern of desquamative interstitial pneumonia, with prominent clustered alveolar macrophages, diffuse reactive alveolar epithelial hyperplasia and globular proteinaceous material, is diagnostic. Desquamative interstitial pneumonia in children can be idiopathic, though it is mostly related to an inborn error of surfactant metabolism. We present the complex clinical course and pathologic findings of a 30-months-old Mauritian and Senegalese girl with idiopathic desquamative interstitial pneumonia and multiple extrapulmonary manifestations. To our knowledge, this is the first case report of desquamative interstitial pneumonia to occur as part of a syndrome with multiple organ involvement. We believe that desquamative interstitial pneumonia is not always associated with mutations of the surfactant proteins, and can still be idiopathic, especially when occurring as part of a syndrome with multiple organ involvement, as described in other interstitial lung diseases

Symmetric Groups and Quotient Complexity of Boolean Operations

The quotient complexity of a regular language L is the number of left quotients of L, which is the same as the state complexity of L. Suppose that L and L' are binary regular languages with quotient complexities m and n, and that the transition semigroups of the minimal deterministic automata accepting L and L' are the symmetric groups S_m and S_n of degrees m and n, respectively. Denote by o any binary boolean operation that is not a constant and not a function of one argument only. For m,n >= 2 with (m,n) not in {(2,2),(3,4),(4,3),(4,4)} we prove that the quotient complexity of LoL' is mn if and only either (a) m is not equal to n or (b) m=n and the bases (ordered pairs of generators) of S_m and S_n are not conjugate. For (m,n)\in {(2,2),(3,4),(4,3),(4,4)} we give examples to show that this need not hold. In proving these results we generalize the notion of uniform minimality to direct products of automata. We also establish a non-trivial connection between complexity of boolean operations and group theory

Syphilis and parvovirus B19 co-infection imitating a lupus nephropathy: A case report.

Syphilis can share clinical features with autoimmune diseases, such as cutaneous Lupus or rheumatoid arthritis. Moreover, secondary syphilis can have visceral involvement, thus affecting the kidney. Syphilitic nephropathy causes nephrotic syndrome with a classic membranous pattern. We present a unique presentation of a co-infection by syphilis and parvovirus B19 sharing all the biological and histological features of proliferative lupus nephritis (LN). We present a case of a 71-year-old Caucasian male returning from a trip to Asia presenting with nephrotic syndrome with antinuclear antibodies (ANA) positivity. Because of nephrotic syndrome a kidney biopsy was performed. It demonstrated a membranous nephropathy with extracapillary proliferation and a full house pattern (presence of IgA, IgG, IgM and C1Q deposits) on immunofluorescence (IF), highly suggestive of LN class III and V. However, several atypical clinical features notably the age, sex of the patient and the history of travel prompt us to search for another cause of nephropathy. A serology was positive for syphilis and a PCR in the renal biopsy was also positive for parvovirus B19. Thus, a co-infection by syphilis and parvovirus B19 was funded to be the cause of the renal lesions. The proteinuria improved; a course of antibiotic was administrated because of neurologic syphilitic involvement (presence of headache with positive syphilis serology in the CSF). A co-infection by syphilis and parvovirus B19 can share all the biological and histological features of proliferative LN and must be recognized as a cause of pseudo-lupus nephritis

Comparison of Fenoterol, Isoproterenol, and Isoetharine with Phenylephrine Aerosol in Asthma

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97253/1/j.1552-4604.1983.tb02708.x.pd

Incidence of glomerulonephritis in the western part of Switzerland over the last decade.

Glomerulonephritis is a rare yet serious group of diseases with a high risk of progression to end-stage renal disease. For optimal healthcare planning, detailed epidemiological and demographic data are essential. Despite their clinical relevance, these data are largely lacking in Switzerland. The objective of this study was to assess the incidence of the different forms of glomerulonephritis in the western part of Switzerland and its changes over the last 10 years, compared with international data. We listed all renal biopsy reports analysed between 2007 and 2016 at the University hospital of Lausanne, the renal pathology reference centre of all hospitals in the cantons of Vaud, Fribourg, Valais and Neuchâtel. Biopsies with a first diagnosis of primary glomerulonephritis were included in the analysis. The incidence was calculated as the number of patients newly diagnosed with glomerulonephritis divided by the number of inhabitants of all the above-mentioned cantons during the year under review, as retrieved from the federal statistical office of Switzerland. We collected biopsy reports from 864 patients between 2007 and 2016; 168 biopsies met the inclusion criteria. The most common primary glomerulonephritis was IgA nephropathy at 32.7% of cases, followed by lupus nephritis (29.8%) and pauci-immune glomerulonephritis (11.9%). Overall, the mean incidence of glomerulonephritis was 1.3/100,000/year. Between 2007 and 2016, the incidence of all glomerulonephritis taken together remained stable. The same was true for the incidence of IgA nephropathy, lupus nephritis and pauci-immune glomerulonephritis. In contrast, we observed a trend towards higher creatinine levels, proteinuria and degree of interstitial fibrosis at diagnosis. The incidence of glomerulonephritis in the western part of Switzerland was low and remained stable over time, in line with European data

Молодежь современной Беларуси: базовые ценности, жизненные планы и поведенческие стратегии

The article considers the transformation of basic values, life plans and behavioral strategies of the youth in contemporary Belarus. The changes in basic values are directly connected with the youth's adaptation to the conditions of global instability. The new generation is sensitive to social injustice, violations of rights and freedoms, unwillingness to take into account their opinions on current issues of social development and the future. The self-perception of people regarding the possibility to realize basic values in the current social-economic conditions is an important factor of social stability. In both 1990 and 2018, family holds the first place among the basic values in Belarus; work takes the second place as a factor of decent life and family's success; the importance of friends and leisure remains the same over the decades, while the importance of politics and religion grows. International comparisons show that Belarus has the same hierarchy of values as European countries. The surveys prove a decrease in popularity of the traditional media among the youth and an increase in individualism, importance of personal self-realization in family and at work, and in reliance on one’s own forces. In the public space, the needs and expectations of people have changed - there is an increase in political radicalization and critical perception of the most important events, which affects the behavioral patterns of social-demographic groups. Education together with the family and new information technologies have a significant impact on values - there is an intragenerational gap, alienation from society and increasing informatization. The article is based on the results of the sociological surveys conducted in the framework of the European Values Study (EVS) (the results of 1990 and 2018 are compared)