On modern computers with graphical user interfaces, application windows are managed by a window manager, a core component of the desktop environment. Mainstream operating systems such as Microsoft Windows and Apple's macOS employ window managers, where users rely on a mouse or trackpad to manually resize, reposition, and switch between overlapping windows. This approach can become inefficient, particularly on smaller screens such as laptops, where frequent window adjustments disrupt workflow and increase task completion time. An alternative paradigm, dynamic window management, automatically arranges application windows into non-overlapping layouts. These systems reduce the need for manual manipulation by providing intelligent placement strategies and support for multiple workspaces. Despite their potential usability benefits, dynamic window managers remain niche, primarily available on Linux systems and rarely enabled by default. This study evaluates the usability of dynamic window managers in comparison to conventional floating window systems. We developed a prototype dynamic window manager that incorporates configurable layouts and workspace management, and we conducted both heur
Time series forecasting (TSF) is crucial in fields like economic forecasting, weather prediction, traffic flow analysis, and public health surveillance. Real-world time series data often include noise, outliers, and missing values, making accurate forecasting challenging. Traditional methods model point-to-point relationships, which limits their ability to capture complex temporal patterns and increases their susceptibility to noise.To address these issues, we introduce the WindowMixer model, built on an all-MLP framework. WindowMixer leverages the continuous nature of time series by examining temporal variations from a window-based perspective. It decomposes time series into trend and seasonal components, handling them individually. For trends, a fully connected (FC) layer makes predictions. For seasonal components, time windows are projected to produce window tokens, processed by Intra-Window-Mixer and Inter-Window-Mixer modules. The Intra-Window-Mixer models relationships within each window, while the Inter-Window-Mixer models relationships between windows. This approach captures intricate patterns and long-range dependencies in the data.Experiments show WindowMixer consistently
Recent works show that hybrid architectures combining local sliding window attention layers and global attention layers outperform either of these architectures taken separately. However, the impact of the window length and the interplay between local layers and global layers remain under-studied. In this work, we first analyze the interaction between short and long term memory by considering SWAX: a hybrid architecture consisting of sliding-window attention and xLSTM linear RNN layers. A counter-intuitive finding is that larger sliding windows hurts the long-context performance. In fact, short window attention encourages the model to better train the long-term memory of the xLSTM as it cannot rely on the local softmax attention mechanism for long context-retrieval. We also validate our findings on local-global architectures alternating short window and full attention layers: the short layers should be small in order not to hinder the usefulness of the long layers. However, employing too small sliding windows is detrimental even for short-context tasks, which could be solved with information from moderately larger sliding windows otherwise. Therefore, we train hybrid architectures
Window decoding, first proposed to reduce decoding complexity for real-time decoding, is an essential component to realize scalable, universal-fault tolerant computation. Prior work has focused on improving throughput through parallelization and reducing reaction time via speculation on window boundaries. However, these methods use a fixed window size d, paying a fixed decoding time overhead for each window. In practice, we find this overhead of a fixed window size unnecessary in many cases due to the sparsity of average-case errors in QEC. Leveraging this insight, in this paper we propose an adaptive window decoding technique based on decoder confidence. This technique reduces the overhead in decoding time thus reducing reaction time without compromising on logical error rates. We benchmark adaptive window decoding across different codes and hardware inspired noise models. Our results show that this adaptive technique reaches the target error rate while maintaining a low decoding time overhead across different codes, and under different noise models.
We develop a general framework for constructing and analyzing overlapping sliding-window statistics for dependence and trend detection. For a fixed window size, the overlapping blocks form a Markov chain, and the asymptotic variance of any centered window statistic is determined by the covariance operator of this chain. Using its spectral structure, we obtain an orthogonal decomposition of the space of window functions into components associated with different overlap levels. This leads to a natural notion of incremental dependence information: the part of a statistic that captures exactly the new information introduced by enlarging the window. We give an explicit procedure for extracting these components and apply the method to two classes of examples. For correlation detection, we study symmetric polynomial window functions and identify their informative projected part. For trend detection, we analyze localized rank-based statistics and isolate the contribution of the largest newly introduced lag. The examples also show that different statistics may exhibit different local detection scales, including nonclassical ones. The same viewpoint leads to a natural quantitative measure of
Windows are used quite frequently in a GUI environment. The greatest advantage of using windows is that each window creates a virtual screen space. Hence, although the physical screen space is limited to a few inches, use of windows can create unlimited screen space to display innumerable items. The use of windows facilitates the user to open and interact with multiple programs or documents simultaneously in different windows. Sometimes a single program may also open multiple windows to display various items. The user can resize the windows and move their location time to time as desired. However, there are several concerns of a window relating to its size, appearance, positioning, color, visibility, resizability etc. For example, the window should have a minimum and a maximum size, dragging and resizing the window should be easy, one window should not be obscured by another window, windows should adjust their size and location in order to match with the changes in the resolution and display environment etc. This article illustrates six patents from US Patent database solving problems relating to displaying and resizing of windows. The inventions include automatic resizing and relo
Recently, a surge of interest in visual transformers is to reduce the computational cost by limiting the calculation of self-attention to a local window. Most current work uses a fixed single-scale window for modeling by default, ignoring the impact of window size on model performance. However, this may limit the modeling potential of these window-based models for multi-scale information. In this paper, we propose a novel method, named Dynamic Window Vision Transformer (DW-ViT). The dynamic window strategy proposed by DW-ViT goes beyond the model that employs a fixed single window setting. To the best of our knowledge, we are the first to use dynamic multi-scale windows to explore the upper limit of the effect of window settings on model performance. In DW-ViT, multi-scale information is obtained by assigning windows of different sizes to different head groups of window multi-head self-attention. Then, the information is dynamically fused by assigning different weights to the multi-scale window branches. We conducted a detailed performance evaluation on three datasets, ImageNet-1K, ADE20K, and COCO. Compared with related state-of-the-art (SoTA) methods, DW-ViT obtains the best perf
In this paper, we introduce the notions of uniform modulo-recurrence and strong modulo-recurrence. We show that Sturmian words and maximal complexity words are strongly modulo-recurrent. Next, a relationship between the window complexity and the classical complexity of the Thue-Morse word is established. We provide an aperiodic recurrent word such that the window complexity is bounded. We also construct a family of aperiodic recurrent words such that their window complexity $P^w(n)$ is in $O(n^α)$, while at least $n^α$ for infinitely many $n$, where $0<α<1$. Finally, we establish that the window complexity of a uniformly recurrent aperiodic word is unbounded.
In many applications like FIR filters, FFT, signal processing and measurements, we are required (~45 dB) or less side lobes amplitudes. However, the problem is usual window based FIR filter design lies in its side lobes amplitudes that are higher than the requirement of application. We propose a window function, which has better performance like narrower main lobe width, minimum side lobe peak compared to the several commonly used windows. The proposed window has slightly larger main lobe width of the commonly used Hamming window, while featuring 6.2\ sim 22.62 dB smaller side lobe peak. The proposed window maintains its maximum side lobe peak about -58.4 \sim -52.6 dB compared to -35.8 \sim -38.8 dB of Hamming window for M=10~14, while offering roughly equal main lobe width. Our simulated results also show significant performance upgrading of the proposed window compared to the Kaiser, Gaussian, and Lanczos windows. The proposed window also shows better performance than Dolph-Chebyshev window. Finally, the example of designed low pass FIR filter confirms the efficiency of the proposed window.
In an arbitrarily varying channel (AVC), the channel has a state which is under the control of an adversarial jammer and the corresponding capacities are often functions of the "power" constraints on the transmitter and jammer. In this paper we propose a model in which the constraints must hold almost surely over contiguous subsequences of the codeword and state, which we call a sliding window constraint. We study oblivious jammers and codes with stochastic encoding under maximum probability of error. We show that this extra limitation on the jammer is beneficial for the transmitter: in some cases, the capacity for unique decoding with a sliding window constraint is equal to the capacity for list decoding in the standard model without sliding windows, roughly implying that the addition of window constraints reduces list decoding to unique decoding. The list decoding capacity in the standard model can be strictly larger than the unique decoding capacity.
We study streaming algorithms for proportionally fair clustering, a notion originally suggested by Chierichetti et. al. (2017), in the sliding window model. We show that although there exist efficient streaming algorithms in the insertion-only model, surprisingly no algorithm can achieve finite multiplicative ratio without violating the fairness constraint in the sliding window. Hence, the problem of fair clustering is a rare separation between the insertion-only streaming model and the sliding window model. On the other hand, we show that if the fairness constraint is relaxed by a multiplicative $(1+\varepsilon)$ factor, there exists a $(1 + \varepsilon)$-approximate sliding window algorithm that uses $\text{poly}(k\varepsilon^{-1}\log n)$ space. This achieves essentially the best parameters (up to degree in the polynomial) provided the aforementioned lower bound. We also implement a number of empirical evaluations on real datasets to complement our theoretical results.
In galaxy survey analysis, the observed clustering statistics do not directly match theoretical predictions but rather have been processed by a window function that arises from the survey geometry including the sky footprint, redshift-dependent background number density and systematic weights. While window convolution of the power spectrum is well studied, for the bispectrum with a larger number of degrees of freedom, it poses a significant numerical and computational challenge. In this work, we consider the effect of the survey window in the tripolar spherical harmonic decomposition of the bispectrum and lay down a formal procedure for their convolution via a series expansion of configuration-space three-point correlation functions, which was first proposed by Sugiyama et al. (2019). We then provide a linear algebra formulation of the full window convolution, where an unwindowed bispectrum model vector can be directly premultiplied by a window matrix specific to each survey geometry. To validate the pipeline, we focus on the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) luminous red galaxy (LRG) sample in the South Galactic Cap (SGC) in the redshift bin $0.4 \le
Image denoising is getting more significance, especially in Computed Tomography (CT), which is an important and most common modality in medical imaging. This is mainly due to that the effectiveness of clinical diagnosis using CT image lies on the image quality. The denoising technique for CT images using window-based Multi-wavelet transformation and thresholding shows the effectiveness in denoising, however, a drawback exists in selecting the closer windows in the process of window-based multi-wavelet transformation and thresholding. Generally, the windows of the duplicate noisy image that are closer to each window of original noisy image are obtained by the checking them sequentially. This leads to the possibility of missing out very closer windows and so enhancement is required in the aforesaid process of the denoising technique. In this paper, we propose a GA-based window selection methodology to include the denoising technique. With the aid of the GA-based window selection methodology, the windows of the duplicate noisy image that are very closer to every window of the original noisy image are extracted in an effective manner. By incorporating the proposed GA-based window selec
We study the space complexity of the following problem: For a fixed regular language $L$, we receive a stream of symbols and want to test membership of a sliding window of size $n$ in $L$. For deterministic streaming algorithms we prove a trichotomy theorem, namely that the (optimal) space complexity is either constant, logarithmic or linear, measured in the window size $n$. Additionally, we provide natural language-theoretic characterizations of the space classes. We then extend the results to randomized streaming algorithms and we show that in this setting, the space complexity of any regular language is either constant, doubly logarithmic, logarithmic or linear. Finally, we introduce sliding window testers, which can distinguish whether a sliding window of size $n$ belongs to the language $L$ or has Hamming distance $> εn$ to $L$. We prove that every regular language has a deterministic (resp., randomized) sliding window tester that requires only logarithmic (resp., constant) space.
Things can go spectacularly wrong when clustering timeseries data that has been preprocessed with a sliding window. We highlight three surprising failures that emerge depending on how the window size compares with the timeseries length. In addition to computational examples, we present theoretical explanations for each of these failure modes.
Attention within windows has been widely explored in vision transformers to balance the performance, computation complexity, and memory footprint. However, current models adopt a hand-crafted fixed-size window design, which restricts their capacity of modeling long-term dependencies and adapting to objects of different sizes. To address this drawback, we propose \textbf{V}aried-\textbf{S}ize Window \textbf{A}ttention (VSA) to learn adaptive window configurations from data. Specifically, based on the tokens within each default window, VSA employs a window regression module to predict the size and location of the target window, i.e., the attention area where the key and value tokens are sampled. By adopting VSA independently for each attention head, it can model long-term dependencies, capture rich context from diverse windows, and promote information exchange among overlapped windows. VSA is an easy-to-implement module that can replace the window attention in state-of-the-art representative models with minor modifications and negligible extra computational cost while improving their performance by a large margin, e.g., 1.1\% for Swin-T on ImageNet classification. In addition, the pe
It is known that windowed decoding (WD) can effectively balance the performance and complexity of spatially coupled low-density parity-check (LDPC) codes. In this study, we show that information can propagate in a wave-like manner at a constant speed under WD. Additionally, we provide an upper bound for the information propagation speed on the binary erasure channel, which can assist in designing the number of iterations required within each window.
For Doppler-broadened media operating under double-double electromagnetically induced transparency (EIT) conditions, we devise a scheme to control and reduce the probe-field group velocity at the center of the second transparency window. We derive numerical and approximate analytical solutions for the width of EIT windows and for the group velocities of the probe field at the two distinct transparency windows, and we show that the group velocities of the probe field can be lowered by judiciously choosing the physical parameters of the system. Our modeling enables us to identify three signal-field strength regimes (with a signal-field strength always higher than the probe-field strength), quantified by the Rabi frequency, for slowing the probe field. These three regimes correspond to a weak signal field, with the probe-field group velocity and transparency window width both smaller for the second window compared to the first window, a medium-strength signal field, with a probe-field group velocity smaller in the second window than in the first window but with larger transparency-window width for the second window, and the strong signal field, with both group velocity and transparenc
In the window mean-payoff objective, given an infinite path, instead of considering a long run average, we consider the minimum payoff that can be ensured at every position of the path over a finite window that slides over the entire path. Chatterjee et al. studied the problem to decide if in a two-player game, Player 1 has a strategy to ensure a window mean-payoff of at least 0. In this work, we consider a function that given a path returns the supremum value of the window mean-payoff that can be ensured over the path and we show how to compute its expected value in Markov chains and Markov decision processes. We consider two variants of the function: Fixed window mean-payoff in which a fixed window length $l_{max}$ is provided; and Bounded window mean-payoff in which we compute the maximum possible value of the window mean-payoff over all possible window lengths. Further, for both variants, we consider (i) a direct version of the problem where for each path, the payoff that can be ensured from its very beginning and (ii) a non-direct version that is the prefix independent counterpart of the direct version of the problem.
The scheme of the sliding window is known in Information Theory, Computer Science, the problem of predicting and in stastistics. Let a source with unknown statistics generate some word $... x_{-1}x_{0}x_{1}x_{2}...$ in some alphabet $A$. For every moment $t, t=... $ $-1, 0, 1, ...$, one stores the word ("window") $ x_{t-w} x_{t-w+1}... x_{t-1}$ where $w$,$w \geq 1$, is called "window length". In the theory of universal coding, the code of the $x_{t}$ depends on source ststistics estimated by the window, in the problem of predicting, each letter $x_{t}$ is predicted using information of the window, etc. After that the letter $x_{t}$ is included in the window on the right, while $x_{t-w}$ is removed from the window. It is the sliding window scheme. This scheme has two merits: it allows one i) to estimate the source statistics quite precisely and ii) to adapt the code in case of a change in the source' statistics. However this scheme has a defect, namely, the necessity to store the window (i.e. the word $x_{t-w}... x_{t-1})$ which needs a large memory size for large $w$. A new scheme named "the Imaginary Sliding Window (ISW)" is constructed. The gist of this scheme is that not the las