On LL-close Sperner systems

For a set $L$ of positive integers, a set system $\mathcal{F} \subseteq 2^{[n]}$ is said to be $L$-close Sperner, if for any pair $F,G$ of distinct sets in $\mathcal{F}$ the skew distance $sd(F,G)=\min\{|F\setminus G|,|G\setminus F|\}$ belongs to $L$. We reprove an extremal result of Boros, Gurvich, and Milani\v c on the maximum size of $L$-close Sperner set systems for $L=\{1\}$ and generalize to $|L|=1$ and obtain slightly weaker bounds for arbitrary $L$. We also consider the problem when $L$ might include 0 and reprove a theorem of Frankl, F\"uredi, and Pach on the size of largest set systems with all skew distances belonging to $L=\{0,1\}$

Liposomes for Use in Gene Delivery

Liposomes have a wide array of uses that have been continuously expanded and improved upon since first being observed to self-assemble into vesicular structures. These arrangements can be found in many shapes and sizes depending on lipid composition. Liposomes are often used to deliver a molecular cargo such as DNA for therapeutic benefit. The lipids used to form such lipoplexes can be cationic, anionic, neutral, or a mixture thereof. Herein physical packing parameters and specific lipids used for gene delivery will be discussed, with lipids classified according to overall charge

Convex Geometry of ReLU-layers, Injectivity on the Ball and Local Reconstruction

The paper uses a frame-theoretic setting to study the injectivity of a ReLU-layer on the closed ball of $\mathbb{R}^n$ and its non-negative part. In particular, the interplay between the radius of the ball and the bias vector is emphasized. Together with a perspective from convex geometry, this leads to a computationally feasible method of verifying the injectivity of a ReLU-layer under reasonable restrictions in terms of an upper bound of the bias vector. Explicit reconstruction formulas are provided, inspired by the duality concept from frame theory. All this gives rise to the possibility of quantifying the invertibility of a ReLU-layer and a concrete reconstruction algorithm for any input vector on the ball.Comment: 10 pages main paper + 2 pages appendix, 4 figures, 2 algorithms, conferenc

Systems biology of energetic and atomic costs in the yeast transcriptome, proteome, and metabolome

Proteins vary in their cost to the cell and natural selection may favour the use of proteins that are cheaper to produce. We develop a novel approach to estimate the amino acid biosynthetic cost based on genome-scale metabolic models, and directly investigate the effects of biosynthetic cost on transcriptomic, proteomic and metabolomic data in _Saccharomyces cerevisiae_. We find that our systems approach to formulating biosynthetic cost produces a novel measure that explains similar levels of variation in gene expression compared with previously reported cost measures. Regardless of the measure used, the cost of amino acid synthesis is weakly associated with transcript and protein levels, independent of codon usage bias. In contrast, energetic costs explain a large proportion of variation in levels of free amino acids. In the economy of the yeast cell, there appears to be no single currency to compute the cost of amino acid synthesis, and thus a systems approach is necessary to uncover the full effects of amino acid biosynthetic cost in complex biological systems that vary with cellular and environmental conditions

Instabilities in Convnets for Raw Audio

What makes waveform-based deep learning so hard? Despite numerous attempts at training convolutional neural networks (convnets) for filterbank design, they often fail to outperform hand-crafted baselines. These baselines are linear time-invariant systems: as such, they can be approximated by convnets with wide receptive fields. Yet, in practice, gradient-based optimization leads to suboptimal approximations. In our article, we approach this phenomenon from the perspective of initialization. We present a theory of large deviations for the energy response of FIR filterbanks with random Gaussian weights. We find that deviations worsen for large filters and locally periodic input signals, which are both typical for audio signal processing applications. Numerical simulations align with our theory and suggest that the condition number of a convolutional layer follows a logarithmic scaling law between the number and length of the filters, which is reminiscent of discrete wavelet bases.Comment: 4 pages, 5 figures, 1 page appendix, under review for IEEE SP

The structure of large logarithmic corrections at small transverse momentum in hadronic collisions

We consider the region of small transverse momenta in the production of high-mass systems in hadronic collisions. By using the current knowledge on the infrared behaviour of tree-level and one-loop QCD amplitudes at O(alpha_s^2), we analytically compute the general form of the logarithmically-enhanced contributions up to next-to-next-to-leading logarithmic accuracy. By comparing the results with q_T-resummation formulae we extract the coefficients that control the resummation of the large logarithmic contributions for both quark and gluon channels. Our results show that within the conventional resummation formalism the Sudakov form factor is actually process-dependent.Comment: 38 pages, 2 figures include

Potrebe u ishrani mlađi štuke (esox lucius) gajene u recirkulacionom sistemu

Zahvaljujući napretku tehnologije, danas je moguće intenzivno gajenje juvenilne štuke u recirkulacionom sistemu korišćenjem formulisane komercijalne hrane (Wolnicki i Górny 1997). Komercijalna hrana koja se trenutno koristi za ishranu štuke je formulisana za druge vrste kao što su pastrmka, som i jesetra. Ova hrana se veoma razlikuje po sastavu proteina i sadržaju energije, što može da utiče na parametre proizvodnje. Smanjivanje odnosa svrarljivosti proteina/energetska efikasnost (DP/DE) u smešama može dovesti do većeg zadržavanja proteina, međutim može imati efekte na zdravlje riba i kvalitet proizvoda. Prvi cilj ove studije je bio da se istraži efekat komercijalnih smeša sa različitom koncentracijom proteina i lipida na juvenilne štuke manje od 20g (eksperiment I) i preko 70g (eksperiment II). Današnji trendovi u proizvodnji hrane za ribe su usmereni u pravcu zamene ribljeg brašna alternativnim izvorima proteina kao što su biljke, suvozemne životinje i nus-proizvodi. Ovi trendovi su dirigovani kako ekonomskim tako i etičkim pitanjima (Brinker and Reiter 2011). Drugi cilj ovog rada je bio da se istraži delimična zamena ribljeg brašna u smešama. U trećem eksperimentu, ispitivana je delimična zamena ribljeg brašna sa pšeničnim glutenom i živinskim brašnom

Time-frequency analysis on flat tori and Gabor frames in finite dimensions

We provide the foundations of a Hilbert space theory for the short-time Fourier transform (STFT) where the flat tori \begin{equation*} \mathbb{T}_{N}^2=\mathbb{R}^2/(\mathbb{Z}\times N\mathbb{Z})=[0,1]\times \lbrack 0,N] \end{equation*} act as phase spaces. We work on an $N$-dimensional subspace $S_{N}$ of distributions periodic in time and frequency in the dual $S_0'(\mathbb{R})$ of the Feichtinger algebra $S_0(\mathbb{R})$ and equip it with an inner product. To construct the Hilbert space $S_{N}$ we apply a suitable double periodization operator to $S_0(\mathbb{R})$. On $S_{N}$, the STFT is applied as the usual STFT defined on $S_0'(\mathbb{R})$. This STFT is a continuous extension of the finite discrete Gabor transform from the lattice onto the entire flat torus. As such, sampling theorems on flat tori lead to Gabor frames in finite dimensions. For Gaussian windows, one is lead to spaces of analytic functions and the construction allows to prove a necessary and sufficient Nyquist rate type result, which is the analogue, for Gabor frames in finite dimensions, of a well known result of Lyubarskii and Seip-Wallst{\'e}n for Gabor frames with Gaussian windows and which, for $N$ odd, produces an explicit \emph{full spark Gabor frame}. The compactness of the phase space, the finite dimension of the signal spaces and our sampling theorem offer practical advantages in some applications. We illustrate this by discussing a problem of current research interest: recovering signals from the zeros of their noisy spectrograms