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We present an approach for designing sources of postselected multipartite states based on photon-pair sources. Our approach can be applied to arbitrary target states in different encoding schemes and physical platforms. It also allows one to limit the types of components to be used in the device, such that lossy or difficult-to-implement optical elements can be avoided. As an example, we apply this strategy to design a passive integrated source of frequency-bin-encoded high-dimensional GHZ states with a 10 kHz on-chip generation rate for picojoule pump pulses.

This paper presents a review of the NTIRE 2024 challenge on night photography rendering. The goal of the challenge was to find solutions that process raw camera images taken in nighttime conditions, and thereby produce a photo-quality output images in the standard RGB (sRGB) space. Unlike the previous year's competition, the challenge images were collected with a mobile phone and the speed of algorithms was also measured alongside the quality of their output. To evaluate the results, a sufficient number of viewers were asked to assess the visual quality of the proposed solutions, considering the subjective nature of the task. There were 2 nominations: quality and efficiency. Top 5 solutions in terms of output quality were sorted by evaluation time (see Fig. 1). The top ranking participants' solutions effectively represent the state-of-the-art in nighttime photography rendering. More results can be found at https://nightimaging.org., Comment: 10 pages, 10 figures

We construct a mixing homeomorphism on the Lelek fan. We also construct a mixing homeomorphism on the Cantor fan. Then, we construct a family of uncountably many pairwise non-homeomorphic (non-)smooth fans that admit a mixing homeomorphism., Comment: arXiv admin note: substantial text overlap with arXiv:2310.19129, arXiv:2309.04003

Let $(X,f)$ be a dynamical system. Using an equivalence relation $\sim$ on $X$, we introduce the quotient $(X/_{\sim},f^{\star})$ of the dynamical system $(X,f)$. In the first part of the paper, we give new results about sensitive dependence on initial conditions of $(X/_{\sim},f^{\star})$, transitivity of $(X/_{\sim},f^{\star})$, and periodic points in $(X/_{\sim},f^{\star})$. In the second part of the paper, we use these results to study chaotic functions on the Cantor fan. Explicitly, we study functions $f$ on the Cantor fan $C$ such that (1) $(C,f)$ is chaotic in the sense of Devaney, (2) $(C,f)$ is chaotic in the sense of Robinson but not in the sense of Devaney, and (3) $(C,f)$ is chaotic in the sense of Knutzen but not in the sense of Devaney. We also study chaos on the Lelek fan.

Recently, many examples of smooth fans that admit a transitive homeomorphism have been constructed. For example, a family of uncountably many pairwise non-homeomorphic smooth fans that admit transitive homeomorphisms was constructed. In this paper, we construct a family of uncountably many pairwise non-homeomorphic non-smooth fans that admit transitive homeomorphisms., Comment: arXiv admin note: text overlap with arXiv:2309.04003, arXiv:2209.07609

We construct a family of uncountably many pairwise non-homeomorphic smooth fans that admit transitive homeomorphisms. In addition, we show that the star of Cantor fans admits a transitive homeomorphism.

In-person human interaction relies on our spatial perception of each other and our surroundings. Current remote communication tools partially address each of these aspects. Video calls convey real user representations but without spatial interactions. Augmented and Virtual Reality (AR/VR) experiences are immersive and spatial but often use virtual environments and characters instead of real-life representations. Bridging these gaps, we introduce DualStream, a system for synchronous mobile AR remote communication that captures, streams, and displays spatial representations of users and their surroundings. DualStream supports transitions between user and environment representations with different levels of visuospatial fidelity, as well as the creation of persistent shared spaces using environment snapshots. We demonstrate how DualStream can enable spatial communication in real-world contexts, and support the creation of blended spaces for collaboration. A formative evaluation of DualStream revealed that users valued the ability to interact spatially and move between representations, and could see DualStream fitting into their own remote communication practices in the near future. Drawing from these findings, we discuss new opportunities for designing more widely accessible spatial communication tools, centered around the mobile phone., Comment: 10 pages, 4 figures, 1 table; To appear in the proceedings of the IEEE International Symposium on Mixed and Augmented Reality (ISMAR) 2023

The Lelek fan $L$ is usually constructed as a subcontinuum of the Cantor fan in such a way that the set of the end-points of $L$ is dense in $L$. It easily follows that the Lelek fan is embeddable into the Cantor fan. {It is also a well-known fact that the Cantor fan is embeddable into the Lelek fan, but this is less obvious. When proving this, one usually uses the well-known result by Dijkstra and van Mill that the Cantor set is embeddable into the complete Erd\"os space, and the well-known fact by Kawamura, Oversteegen, and Tymchatyn that the set of end-points of the Lelek fan is homeomorphic to the complete Erd\"os space. Then, the subcontinuum of the Lelek fan that is induced by the embedded Cantor set into the set of end-points of the Lelek fan, is a Cantor fan. In our paper, we give an alternative straightforward construction of a Cantor fan into the Lelek fan. We do not use the fact that the Cantor set is embeddable into the complete Erd\"os space and that it is homeomorphic to the set of end-points of the Lelek fan. Instead, we use our recent techniques of Mahavier products of closed relations to produce an embedding of the Cantor fan into the Lelek fan. Since the Cantor fan is universal for the family of all smooth fans, it follows that also the Lelek fan is universal for smooth fans.

We demonstrate that genuine multipartite entangled states can be generated using frequency bin encoding in integrated photonic platforms. We introduce a source of four-photon GHZ states, and a source of three-photon W states. We predict generation rates on the order of 10$^4$ Hz for a silicon microring source with milliwatt pump powers. These results, along with the versatility and scalability of integrated structures, identify this as a promising approach for the generation of higher-dimensional and larger entangled states.

Many continua that admit a transitive homeomorphism may be found in the literature. The circle is probably the simplest non-degenerate continuum that admits such a homeomorphism. On the other hand, most of the known examples of such continua have a complicated topological structure. For example, they are {indecomposable} (such as the pseudo-arc or the Knaster bucket-handle continuum), or they are {not indecomposable} but have some other complicated topological structure, such as a dense set of ramification points (such as the Sierpi\' nski carpet) or a dense set of end-points (such as the Lelek fan). In this paper, we continue our mission of finding continua with simpler topological structures that admit a transitive homeomorphism.} We construct a transitive homeomorphism on the Cantor fan. {In our approach, we use four different techniques, each of them giving a unique construction of a transitive homeomorphism on the Cantor fan:} two techniques using quotient spaces of products of compact metric spaces and Cantor sets, and two using Mahavier products of closed relations on compact metric spaces. {We also demonstrate how our technique using Mahavier products of closed relations may be used to } construct a transitive function $f$ on a Cantor fan $X$ such that $\varprojlim(X,f)$ is a Lelek fan.

We present a method of tomography that measures the joint spectral phase (JSP) of spontaneously emitted photon pairs originating from a largely uncharacterized ``target" source. We use quantum interference between our target source and a reference source to extract the JSP with four spectrally resolved measurements, in a process that we call quantum-referenced spontaneous emission tomography (Q-SpET). We have demonstrated this method on a photonic integrated circuit for a target micro-ring resonator photon-pair source. Our results show that spontaneously emitted photon pairs from a micro-ring resonator are distinctively different from that of stimulated emission, and thus cannot in general be fully characterized using classical stimulated emission tomography without detailed knowledge of the source.

We introduce the notions of returns, dispersions and well-aligned sets for closed relations on compact metric spaces and then we use them to obtain non-trivial sufficient conditions for such a relation to have non-zero entropy. In addition, we give a characterization of finite relations with non-zero entropy in terms of Li-Yorke and DC2-chaos.

Let $X$ be a continuum and let $\varphi:X\rightarrow X$ be a homeomorphism. To construct a dynamical system $(X,\varphi)$ with interesting dynamical properties, the continuum $X$ often needs to have some complicated topological structure. In this paper, we are interested in one such dynamical property: transitivity. By now, various examples of continua $X$ have been constructed in such a way that the dynamical system $(X,\varphi)$ is transitive. Mostly, they are examples of continua that are not path-connected, such as the pseudo-arc or the pseudo-circle, or they are examples of locally connected continua (and every locally connected continuum is path-connected), Wazewski's universal dendrite and the Sierpinski carpet are such examples. In this paper, we present an example of a dynamical system $(X,\varphi)$, where $\varphi$ is a homeomorphism on the continuum $X$ and $X$ is a path-connected but not locally connected continuum. We construct a transitive homeomorphism on the Lelek fan. As a by-product, a non-invertible transitive map on the Lelek fan is also constructed., Comment: arXiv admin note: text overlap with arXiv:2206.00087

We study different types of transitive points in CR-dynamical systems (X,G) with closed relations G on compact metric spaces X. We also introduce transitive and dense orbit transitive CR-dynamical systems and discuss their properties and the relations between them. This generalizes the notion of transitive topological dynamical systems (X, f ).

We consider a family of inverse limits of inverse sequences of closed unit intervals with a single upper semi-continuous set-valued bonding function whose graph is an arc; it is the union of two line segments in $[0,1]^2$, both of them contain the origin $(0, 0)$, have positive slope, and extend to the opposite boundary of $[0,1]^2$. We show that there is a large subfamily $\mathcal F$ of these bonding functions such that for each $f\in \mathcal F$, the inverse limit of the inverse sequence of closed unit intervals using $f$ as a single bonding function, is homeomorphic to the Lelek fan.

We introduce dynamical systems $(X,G)$ with closed relations $G$ on compact metric spaces $X$ and discuss different types of minimality of such dynamical systems, all of them generalizing minimal dynamical systems $(X,f)$ with continuous function $f$ on a compact metric space $X$.

Third order parametric down-conversion describes a class of nonlinear processes in which a pump photon can be down-converted into triplets of photons. It has been identified as a source of non-classical light, with capabilities beyond those offered by better-established processes such as spontaneous four-wave mixing. Here we discuss the implementation of TOPDC in integrated photonic systems. We derive equations for the rates of TOPDC in a non-resonant (waveguide) and resonant (microring) platform, such that the scaling with experimental parameters can be plainly seen. We find that generally non-resonant platforms should be pursued for spontaneous TOPDC (SpTOPDC), whereas resonant platforms are more suitable for stimulated TOPDC (StTOPDC). We present a sample calculation for TOPDC rates in sample systems with conservative and accessible parameters. We find that StTOPDC should be observable with the current fabrication technology, and that with some progress in the design of TOPDC platforms, integrated SpTOPDC too could be demonstrated in the near term.

The paper is motivated by E. Akin's book about dynamical systems and closed relations [A], and by J. Kennedy's and G. Erceg's recent paper about the entropy of closed relations on closed intervals [EK]. In present paper, we introduce the entropy of a closed relation G on any compact metric space X and show its basic properties. We also introduce when such a relation G generates a periodic point or finitely generates a Cantor set. Then we show that periodic points, finitely generated Cantor sets, Mahavier products and the entropy of closed relations are preserved by topological conjugations. Among other things, this generalizes the well-known results about the topological conjugacy of continuous mappings. Finally, we prove a theorem, giving sufficient conditions for a closed relation G on [0,1] to have a non-zero entropy. Then we present various examples of closed relations G on [0,1] such that (1) the entropy of G is non-zero, (2) no periodic point or exactly one periodic point is generated by G, and (3) no Cantor set is finitely generated by G.

Among other results, the paper gives new mapping theorems and new fixed point property theorems for inverse limits of inverse sequences of compact metric spaces with upper semicontinuous set-valued bonding functions. We also revisit the results from two papers, Mioduszewski's ''Mappings of inverse limits'' and Feuerbacher's ''Mappings of inverse limits revisited''.

We present two complementary strategies for modeling nonlinear quantum optics in realistic integrated optical devices, where scattering loss is present. In the first strategy, we model scattering loss as an attenuation; in the second, we employ a Hamiltonian treatment that includes a mechanism for scattering loss, such as a `phantom waveguide.' These strategies can be applied to a broad range of structures and processes. As an example, we use these two approaches to model spontaneous four-wave mixing in (i) a ring-channel system and (ii) an add-drop system. Even for these well-understood systems, our strategies yield some novel results. We show the rates of photon pairs, broken pairs, and lost pairs and their dependence on system parameters. We show that the properties of lost and broken photon pairs in such structures can be related to those of the un-scattered photon pairs, which are relatively simple to measure.

Inspired by Lelek's idea from [Disjoint mappings and the span of spaces, Fund. Math. 55 (1964), 199 -- 214], we introduce the novel notion of the span of graphs. Using this, we solve the problem of determining the \emph{maximal safety distance} two players can keep at all times while traversing a graph. Moreover, their moves must be made with respect to certain move rules. For this purpose, we introduce different variants of a span of a given connected graph. All the variants model the maximum safety distance kept by two players in a graph traversal, where the players may only move with accordance to a specific set of rules, and their goal: visit either all vertices, or all edges. For each variant, we show that the solution can be obtained by considering only connected subgraphs of a graph product and the projections to the factors. We characterise graphs in which it is impossible to keep a positive safety distance at all moments in time. Finally, we present a polynomial time algorithm that determines the chosen span variant of a given graph., Comment: Discrete Mathematics and Theoretical Computer Science vol. 25:1 #8 (2023)

In this paper, we respond to a critique of one of our papers previously published in this journal, entitled "TVOR: Finding Discrete Total Variation Outliers among Histograms". Our paper proposes a method for smoothness outliers detection among histograms by using the relation between their discrete total variations (DTV) and their respective sample sizes. In this response, we demonstrate point by point that, contrary to its claims, the critique has not found any mistakes or problems in our paper, either in the used datasets, methodology, or in the obtained top outlier candidates. On the contrary, the critique's claims can easily be shown to be mathematically unfounded, to directly contradict the common statistical theorems, and to go against well established demographic terms. Exactly this is done in the reply here by providing both theoretical and experimental evidence. Additionally, due to critique's complaint, a more extensive research on top outlier candidate, i.e. the Jasenovac list is conducted and in order to clear any of the critique's doubts, new evidence of its problematic nature unseen in other lists are presented. This reply is accompanied by additional theoretical explanations, simulations, and experimental results that not only confirm the earlier findings, but also present new data. The source code is at https://github.com/DiscreteTotalVariation/TVOR., Comment: 63 pages, 7 figures

We give two characterizations of $\mathcal P$-like continua $X$ that do not have the fixed point property. Both characterizations are stated in terms of sequences of open covers of $X$ that follow fixed-point-free patterns. We use these to characterize planar tree-like continua that do not have the fixed point property in terms of infinite sequences of tree-chains in the plane that follow fixed-point-free patterns. We also establish a useful relationship between these tree-chains and commutative simplicial diagrams that we use later to construct a finite sequence (of any given length) of tree-chains in the plane that follows a fixed-point-free pattern. An earlier characterization of $\mathcal P$-like continua with the fixed point property was given in 1994 by Feuerbacher based on a 1963 result by Mioduszewski. The Mioduszewski-Feuerbacher characterization is expressed in terms of almost commutative inverse diagrams. In contrast, our approach is more geometric, and it may potentially lead to new methods in the elusive search for a planar tree-like continuum without the fixed-point property.

Third-order parametric down-conversion (TOPDC) describes a class of nonlinear interactions in which a pump photon is converted into a photon triplet. This process can occur spontaneously, or it can be stimulated by seeding fields. In the former case, one typically has the generation of non-Gaussian states of light. In the latter, the situation is more variegated, for stimulated TOPDC (StTOPDC) can be implemented in many ways, depending on the number and properties of the seeding fields. Here we show that StTOPDC can be exploited for the generation of quantum correlated photon pairs. We examine the peculiar features of this approach when compared with second-order spontaneous parametric down-conversion and spontaneous four-wave mixing. We model StTOPDC in a microring resonator, predicting observable generation rates in a microring engineered for third-harmonic generation. We conclude that if the experimental difficulties associated with implementing StTOPDC can be overcome, it may soon be possible to demonstrate this process in resonant integrated devices.

Illumination estimation is the essential step of computational color constancy, one of the core parts of various image processing pipelines of modern digital cameras. Having an accurate and reliable illumination estimation is important for reducing the illumination influence on the image colors. To motivate the generation of new ideas and the development of new algorithms in this field, the 2nd Illumination estimation challenge~(IEC\#2) was conducted. The main advantage of testing a method on a challenge over testing in on some of the known datasets is the fact that the ground-truth illuminations for the challenge test images are unknown up until the results have been submitted, which prevents any potential hyperparameter tuning that may be biased. The challenge had several tracks: general, indoor, and two-illuminant with each of them focusing on different parameters of the scenes. Other main features of it are a new large dataset of images (about 5000) taken with the same camera sensor model, a manual markup accompanying each image, diverse content with scenes taken in numerous countries under a huge variety of illuminations extracted by using the SpyderCube calibration object, and a contest-like markup for the images from the Cube+ dataset that was used in IEC\#1. This paper focuses on the description of the past two challenges, algorithms which won in each track, and the conclusions that were drawn based on the results obtained during the 1st and 2nd challenge that can be useful for similar future developments.

Pearson's chi-squared test can detect outliers in the data distribution of a given set of histograms. However, in fields such as demographics (for e.g. birth years), outliers may be more easily found in terms of the histogram smoothness where techniques such as Whipple's or Myers' indices handle successfully only specific anomalies. This paper proposes smoothness outliers detection among histograms by using the relation between their discrete total variations (DTV) and their respective sample sizes. This relation is mathematically derived to be applicable in all cases and simplified by an accurate linear model. The deviation of the histogram's DTV from the value predicted by the model is used as the outlier score and the proposed method is named Total Variation Outlier Recognizer (TVOR). TVOR requires no prior assumptions about the histograms' samples' distribution, it has no hyperparameters that require tuning, it is not limited to only specific patterns, and it is applicable to histograms with the same bins. Each bin can have an arbitrary interval that can also be unbounded. TVOR finds DTV outliers easier than Pearson's chi-squared test. In case of distribution outliers, the opposite holds. TVOR is tested on real census data and it successfully finds suspicious histograms. The source code is given at https://github.com/DiscreteTotalVariation/TVOR., Comment: 28 pages, 25 figures

Computational color constancy has the important task of reducing the influence of the scene illumination on the object colors. As such, it is an essential part of the image processing pipelines of most digital cameras. One of the important parts of the computational color constancy is illumination estimation, i.e. estimating the illumination color. When an illumination estimation method is proposed, its accuracy is usually reported by providing the values of error metrics obtained on the images of publicly available datasets. However, over time it has been shown that many of these datasets have problems such as too few images, inappropriate image quality, lack of scene diversity, absence of version tracking, violation of various assumptions, GDPR regulation violation, lack of additional shooting procedure info, etc. In this paper, a new illumination estimation dataset is proposed that aims to alleviate many of the mentioned problems and to help the illumination estimation research. It consists of 4890 images with known illumination colors as well as with additional semantic data that can further make the learning process more accurate. Due to the usage of the SpyderCube color target, for every image there are two ground-truth illumination records covering different directions. Because of that, the dataset can be used for training and testing of methods that perform single or two-illuminant estimation. This makes it superior to many similar existing datasets. The datasets, it's smaller version SimpleCube++, and the accompanying code are available at https://github.com/Visillect/CubePlusPlus/.

Resonant mm-wave fields drive $n_0f(2) \rightarrow (n_0 \pm 1)g(2)$ transitions in a state-selected $n_0f(2)$ Rydberg gas of NO. This transformation produces a clear signature in the selected field ionization spectrum and dramatically increases the intensity of corresponding features in the spectrum of the $n_0f(2)$ Rydberg series observed in UV-UV double resonant transitions via the $A ~^2\Sigma^+, ~N'=0$ state. Here, $n_0$ refers to the principal quantum number of an $f$ Rydberg state converging to the $N^+=2$ rotational state of NO$^+ X~ ^1\Sigma^+$. Enhancement owing to transitions from $\ell=3$ ($f$) to $\ell=4$ ($g$) appears both in the electron signal detected at early time by the field ionization of Rydberg molecules and, 40 $\mu$s later, as the late-peak signal of plasma in a state of arrested relaxation. Similar stabilization and enhanced intensity also occurs for shorter-lived interloping complex resonances, $44p(0) - 43d(1)$ and $43p(0) - 42d(1)$. We conclude from these observations that avalanche alone does not guarantee a plasma state of arrested relaxation. But rather, the formation of an arrested phase requires both avalanche-produced NO$^+$ ions and a persistent population of long-lived Rydberg molecules.

Implementing color constancy as a pre-processing step in contemporary digital cameras is of significant importance as it removes the influence of scene illumination on object colors. Several benchmark color constancy datasets have been created for the purpose of developing and testing new color constancy methods. However, they all have numerous drawbacks including a small number of images, erroneously extracted ground-truth illuminations, long histories of misuses, violations of their stated assumptions, etc. To overcome such and similar problems, in this paper a color constancy benchmark dataset generator is proposed. For a given camera sensor it enables generation of any number of realistic raw images taken in a subset of the real world, namely images of printed photographs. Datasets with such images share many positive features with other existing real-world datasets, while some of the negative features are completely eliminated. The generated images can be successfully used to train methods that afterward achieve high accuracy on real-world datasets. This opens the way for creating large enough datasets for advanced deep learning techniques. Experimental results are presented and discussed. The source code is available at http://www.fer.unizg.hr/ipg/resources/color_constancy/., Comment: 10 pages, 8 figures

The pipelines of digital cameras contain a part for computational color constancy, which aims to remove the influence of the illumination on the scene colors. One of the best known and most widely used benchmark datasets for this problem is the Color Checker dataset. However, due to the improper handling of the black level in its images, this dataset has been widely misused and while some recent publications tried to alleviate the problem, they nevertheless erred and created additional wrong data. This paper gives a history of the Color Checker dataset usage, it describes the origins and reasons for its misuses, and it explains the old and new mistakes introduced in the most recent publications that tried to handle the issue. This should, hopefully, help to prevent similar future misuses., Comment: 5 pages, 4 figures