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$\theta$ intermediate dimensions are a continuous family of dimensions that interpolate between Hausdorff and Box dimensions of fractal sets. In this paper we study the problem of the relationship between the dimension of a set $E\subset\mathbb{R}^d$ and the dimension of the slices $E\cap V$ from the point of view of intermediate dimensions. Here $V\in G(d,m)$, where $G(d,m)$ is the set of $m-$dimensional subspaces of $\mathbb{R}^d$. We obtain upper bounds analogous to those already known for Hausdorff dimension. In addition, we prove several corollaries referring to, among other things, the continuity of these dimensions at $\theta=0$, a natural problem that arises when studying them. We also investigate which conditions are sufficient to obtain a lower bound that provides an equality for almost all slices. Finally, a new type of Frostman measures is introduced. These measures combine the results already known for intermediate dimensions and Frostman measures in the case of Hausdorff dimension.

In this paper, we define a family of dimensions for Borel measures that lie between the Hausdorff and Minkowski dimensions for measures, analogous to the intermediate dimensions of sets. Previously, Hare et. al. in [10] defined intermediate dimensions that interpolate between the Minkowski and Assouad dimensions for measures. Additionally, Fraser, in [7] introduced intermediate dimensions that interpolate between the Fourier and Hausdorff dimensions of measures. Our results address a "gap" in the study of dimension interpolation for measures, almost completing the spectrum of intermediate dimensions for measures: from Fourier to Assouad dimensions. Furthermore, Theorem 3.11 can be interpreted as a "reverse Frostman" lemma for intermediate dimensions. We also obtain a capacity-theoretic definition that enables us to estimate the intermediate dimensions of pushforward measures by projections.

Given a compact set $E\subset\mathbb{R}^d$ we investigate for which values of $m$ we have that $\dim_\theta P_V(E)=m$ or $\dim_\theta P_V(E)=\dim_\theta E$ for $\gamma_{d,m}-$almost all $V\in G(d,m)$. Our result can be extended to more general functions that include orthogonal projections and fractional Brownian motion. As a particular case, letting $\theta=1$, the results are valid for the Box dimension.

The next-generation Very Large Array (ngVLA) is intended to be the premier centimeter-wavelength facility for astronomy and astrophysics, building on the substantial scientific legacies of the Karl G. Jansky Very Large Array (VLA) and the Very Long Baseline Array (VLBA). The ngVLA would open a new window on the Universe through ultra-sensitive imaging of thermal line and continuum emission to milliarcsecond resolution, while delivering unprecedented broad-band continuum imaging and polarimetry of non-thermal emission. The ngVLA would provide a critical electromagnetic complement to a suite of particle detectors and gravitational-wave observatories, as well as space- and ground-based telescopes operating from infrared to gamma-ray wavelengths, hence enabling multi-messenger and multi-band astronomy and astrophysics. Current construction plans call for the ngVLA to leverage some of the physical infrastructure of both the VLA and the VLBA, potentially drawing on overlapping personnel and information infrastructure. Multiple options can be envisioned for a VLA+VLBA to ngVLA transition. In order to assess risks and benefits of possible transition plans, the ngVLA project established the VLA+VLBA to ngVLA Transition Advisory Group (TAG). The primary deliverable from the TAG is a ``VLA+VLBA to ngVLA Transition Option Concepts'' report (this report) that includes a prioritized list of transition options., Comment: This report reflects an initial set of recommendations by the Transition Advisory Group for the ngVLA Project and is distributed for the purposes of obtaining community comment. Modification of this report in response to community comment is expected. Please submit your feedback at ngvla-transition-feedback@listmgr.nrao.edu

Given a positive, non-increasing sequence $a$ with a finite sum $L$, we consider all the closed subsets of $[0,L]$ such that the lengths of their complementary open intervals are a rearrangement of the sequence $a$. We study all possible $\theta$-intermediate dimensions for these sets and show that, under some assumptions, it is an interval.

Knockout tournaments, also known as single-elimination or cup tournaments, are a popular form of sports competitions. In the standard probabilistic setting, for each pairing of players, one of the players wins the game with a certain (a priori known) probability. Due to their competitive nature, tournaments are prone to manipulation. We investigate the computational problem of determining whether, for a given tournament, a coalition has a manipulation strategy that increases the winning probability of a designated player above a given threshold. More precisely, in every round of the tournament, coalition players can strategically decide which games to throw based on the advancement of other players to the current round. We call this setting adaptive constructive coalition manipulation. To the best of our knowledge, while coalition manipulation has been studied in the literature, this is the first work to introduce adaptiveness to this context. We show that the above problem is hard for every complexity class in the polynomial hierarchy. On the algorithmic side, we show that the problem is solvable in polynomial time when the coalition size is a constant. Furthermore, we show that the problem is fixed-parameter tractable when parameterized by the coalition size and the size of a minimum player set that must include at least one player from each non-deterministic game. Lastly, we investigate a generalized setting where the tournament tree can be imbalanced.

Measuring terahertz waveforms in terahertz spectroscopy often relies on electro optic sampling employing a ZnTe crystal. Although the nonlinearities in such zincblende semiconductors induced by intense terahertz pulses have been studied at optical frequencies, the manifestation of nonlinearity in the terahertz regime has not been reported. In this work, we investigate the nonlinear response of ZnTe in the terahertz frequency region utilizing time-resolved terahertz-pump terahertz-probe spectroscopy. We find that the interaction of two co-propagating terahertz pulses in ZnTe leads to a nonlinear polarization change which modifies the electro-optic response of the medium. We present a model for this polarization that showcases the second-order nonlinear behavior. We also determine the magnitude of the third-order susceptibility in ZnTe at terahertz frequencies, $\chi^{\mathrm{(3)}}(\omega_\text{THz})$. These results clarify the interactions in ZnTe at terahertz frequencies, with implications for measurements of intense terahertz fields using electro-optic sampling., Comment: 11 pages, 6 figures

We study the fundamental scheduling problem $1\mid r_j\mid\sum w_j U_j$: schedule a set of $n$ jobs with weights, processing times, release dates, and due dates on a single machine, such that each job starts after its release date and we maximize the weighted number of jobs that complete execution before their due date. Problem $1\mid r_j\mid\sum w_j U_j$ generalizes both Knapsack and Partition, and the simplified setting without release dates was studied by Hermelin et al. [Annals of Operations Research, 2021] from a parameterized complexity viewpoint. Our main contribution is a thorough complexity analysis of $1\mid r_j\mid\sum w_j U_j$ in terms of four key problem parameters: the number $p_\#$ of processing times, the number $w_\#$ of weights, the number $d_\#$ of due dates, and the number $r_\#$ of release dates of the jobs. $1\mid r_j\mid\sum w_j U_j$ is known to be weakly para-NP-hard even if $w_\#+d_\#+r_\#$ is constant, and Heeger and Hermelin [ESA, 2024] recently showed (weak) W[1]-hardness parameterized by $p_\#$ or $w_\#$ even if $r_\#$ is constant. Algorithmically, we show that $1\mid r_j\mid\sum w_j U_j$ is fixed-parameter tractable parameterized by $p_\#$ combined with any two of the remaining three parameters $w_\#$, $d_\#$, and $r_\#$. We further provide pseudo-polynomial XP-time algorithms for parameter $r_\#$ and $d_\#$. To complement these algorithms, we show that $1\mid r_j\mid\sum w_j U_j$ is (strongly) W[1]-hard when parameterized by $d_\#+r_\#$ even if $w_\#$ is constant. Our results provide a nearly complete picture of the complexity of $1\mid r_j\mid\sum w_j U_j$ for $p_\#$, $w_\#$, $d_\#$, and $r_\#$ as parameters, and extend those of Hermelin et al. [Annals of Operations Research, 2021] for the problem $1\mid\mid\sum w_j U_j$ without release dates.

In this paper, we examine a discrete dynamical system defined by x(n+1) = Ax(n)+ w(n), where x takes values in a Hilbert space H and w is a periodic source with values in a fixed closed subspace W of H. Our goal is to identify conditions on some spatial sampling system G = {gj: j in J} of H that enable stable recovery of the unknown source term w from space-time samples {: n >=0,j in J}. We provide necessary and sufficient conditions on G = {g_j }_{j in J} to ensure stable recovery of any w in W . Additionally, we explicitly construct an operator R, dependent on G, such that R{}_n,j} = w., Comment: 12 pages

Quantum imaging with undetected photons spatially transfers amplitude and phase information from one spectral region of physical interest to another spectral region that is easy to detect. The photon energy of the two spectral regions can, in principle, be separated by several orders of magnitude. However, quantum imaging with undetected photons has so far only been demonstrated in spectral regions of similar order of magnitude in frequency (and for which cameras are commercially available). Here, we demonstrate amplitude- and phase-sensitive imaging in the terahertz spectral region (1.5 THz center frequency) by detecting only visible photons (center wavelength 662.2 nm, 452.7 THz center frequency) more than two orders of magnitude apart. As a result, terahertz spectral information can be reliably detected with a standard CMOS camera without cooling, achieving a spatial resolution close to the wavelength. By taking advantage of quantum distillation in a nonlinear interferometer, the influence of ubiquitous thermal terahertz photons can be neglected. Our results are in good agreement with numerical simulations of the imaging process and demonstrate the huge potential of this method to address otherwise challenging spectral regions where cameras do not exist.

Fair resource allocation is undoubtedly a crucial factor in customer satisfaction in several scheduling scenarios. This is especially apparent in repetitive scheduling models where the same set of clients repeatedly submits jobs on a daily basis. In this paper, we aim to analyze a repetitive scheduling system involving a set of $n$ clients and a set of $m$ days. On every day, each client submits a request to process a job exactly within a specific time interval, which may vary from day to day, modeling the scenario where the scheduling is done Just-In-Time (JIT). The daily schedule is executed on a single machine that can process a single job at a time, therefore it is not possible to schedule jobs with intersecting time intervals. Accordingly, a feasible solution corresponds to sets of jobs with disjoint time intervals, one set per day. We define the quality of service (QoS) that a client receives as the number of executed jobs over the $m$ days period. Our objective is to provide a feasible solution where each client has at least $k$ days where his jobs are processed. We prove that this problem is NP-hard even under various natural restrictions such as identical processing times and day-independent due dates. We also provide efficient algorithms for several special cases and analyze the parameterized tractability of the problem with respect to several parameters, providing both parameterized hardness and tractability results.

In this work, we study the computational (parameterized) complexity of $P \mid r_j, p_j=p \mid \sum_j w_j U_j$. Here, we are given $m$ identical parallel machines and $n$ jobs with equal processing time, each characterized by a release date, a due date, and a weight. The task is to find a feasible schedule, that is, an assignment of the jobs to starting times on machines, such that no job starts before its release date and no machine processes several jobs at the same time, that minimizes the weighted number of tardy jobs. A job is considered tardy if it finishes after its due date. Our main contribution is showing that $P \mid r_j, p_j=p \mid \sum_j U_j$ (the unweighted version of the problem) is NP-hard and W[2]-hard when parameterized by the number of machines. The former resolves an open problem in Note 2.1.19 by Kravchenko and Werner [Journal of Scheduling, 2011] and Open Problem 2 by Sgall [ESA, 2012], and the latter resolves Open Problem 7 by Mnich and van Bevern [Computers & Operations Research, 2018]. Furthermore, our result shows that the known XP-algorithm for $P \mid r_j, p_j=p \mid \sum_j w_j U_j$ parameterized by the number of machines is optimal from a classification standpoint. On the algorithmic side, we provide alternative running time bounds for the above-mentioned known XP-algorithm. Our analysis shows that $P \mid r_j, p_j=p \mid \sum_j w_j U_j$ is contained in XP when parameterized by the processing time, and that it is contained in FPT when parameterized by the combination of the number of machines and the processing time. Finally, we give an FPT-algorithm for $P \mid r_j, p_j=p \mid \sum_j w_j U_j$ parameterized by the number of release dates or the number of due dates. With this work, we lay out the foundation for a systematic study of the parameterized complexity of $P \mid r_j, p_j=p \mid \sum_j w_j U_j$.

This paper explores woven frames in separable Hilbert spaces with an initial focus on the finite-dimensional case. We begin by simplifying the problem to bases, for which we obtain a unique characterization. We establish a condition that is both necessary and sufficient for vector reconstruction, which applies to Fourier matrices. Furthermore, we show that these characterizations are still valid in the infinite-dimensional case, for Riesz bases. Finally, we obtain several results for weaving Riesz bases of translations., Comment: 15 pages, to appear Journal of Fourier Analysis and Applications

In this paper, we study the complexity of the \textit{periodic temporal graph realization} problem with respect to upper bounds on the fastest path durations among its vertices. This constraint with respect to upper bounds appears naturally in transportation network design applications where, for example, a road network is given, and the goal is to appropriately schedule periodic travel routes, while not exceeding some desired upper bounds on the travel times. This approach is in contrast to verification applications of the graph realization problems, where exact values for the distances (respectively, fastest travel times) are given, following some kind of precise measurement. In our work, we focus only on underlying tree topologies, which are fundamental in many transportation network applications. As it turns out, the periodic upper-bounded temporal tree realization problem (TTR) has a very different computational complexity behavior than both (i) the classic graph realization problem with respect to shortest path distances in static graphs and (ii) the periodic temporal graph realization problem with exact given fastest travel times (which was recently introduced). First, we prove that, surprisingly, TTR is NP-hard, even for a constant period $\Delta$ and when the input tree $G$ satisfies at least one of the following conditions: (a) $G$ has a constant diameter, or (b) $G$ has constant maximum degree. In contrast, when we are given exact values of the fastest travel delays, the problem is known to be solvable in polynomial time. Second, we prove that TTR is fixed-parameter tractable (FPT) with respect to the number of leaves in the input tree $G$, via a novel combination of techniques for totally unimodular matrices and mixed integer linear programming.

Challenge the champ tournaments are one of the simplest forms of competition, where a (initially selected) champ is repeatedly challenged by other players. If a player beats the champ, then that player is considered the new (current) champ. Each player in the competition challenges the current champ once in a fixed order. The champ of the last round is considered the winner of the tournament. We investigate a setting where players can be bribed to lower their winning probability against the initial champ. The goal is to maximize the probability of the initial champ winning the tournament by bribing the other players, while not exceeding a given budget for the bribes. Mattei et al. [Journal of Applied Logic, 2015] showed that the problem can be solved in pseudo-polynomial time, and that it is in XP when parameterized by the number of players. We show that the problem is weakly NP-hard and W[1]-hard when parameterized by the number of players. On the algorithmic side, we show that the problem is fixed-parameter tractable when parameterized either by the number of different bribe values or the number of different probability values. To this end, we establish several results that are of independent interest. In particular, we show that the product knapsack problem is W[1]-hard when parameterized by the number of items in the knapsack, and that constructive bribery for cup tournaments is W[1]-hard when parameterized by the number of players. Furthermore, we present a novel way of designing mixed integer linear programs, ensuring optimal solutions where all variables are integers.

JWST measured the infrared spectra of Saturn's rings and several of its small moons (Epimetheus, Pandora, Telesto and Pallene) as part of Guaranteed Time Observation program 1247. The NIRSpec instrument obtained near-infrared spectra of the small moons between 0.6 and 5.3 microns, which are all dominated by water-ice absorption bands. The shapes of the water-ice bands for these moons suggests that their surfaces contain variable mixes of crystalline and amorphous ice or variable amounts of contaminants and/or sub-micron ice grains. The near-infrared spectrum of Saturn's A ring has exceptionally high signal-to-noise between 2.7 and 5 microns and is dominated by features due to highly crystalline water ice. The ring spectrum also confirms that the rings possess a 2-3% deep absorption at 4.13 microns due to deuterated water-ice previously seen by the Visual and Infrared Mapping Spectrometer onboard the Cassini spacecraft. This spectrum also constrains the fundamental absorption bands of carbon dioxide and carbon monoxide and may contain evidence for a weak aliphatic hydrocarbon band. Meanwhile, the MIRI instrument obtained mid-infrared spectra of the rings between 4.9 and 27.9 microns, where the observed signal is a combination of reflected sunlight and thermal emission. This region shows a strong reflectance peak centered around 9.3 microns that can be attributed to crystalline water ice. Since both the near and mid-infrared spectra are dominated by highly crystalline water ice, they should provide a useful baseline for interpreting the spectra of other objects in the outer solar system with more complex compositions., Comment: Accepted for Publication in JGR Planets

Resistivity is one of the most important characteristics in the semiconductor industry. The most common way to measure resistivity is the four-point probe method, which requires physical contact with the material under test. Terahertz time domain spectroscopy, a fast and non-destructive measurement method, is already well established in the characterization of dielectrics. In this work, we demonstrate the potential of two Drude model-based approaches to extract resistivity values from terahertz time-domain spectroscopy measurements of silicon in a wide range from about 10$^{-3}$ $\Omega$cm to 10$^{2}$ $\Omega$cm. One method is an analytical approach and the other is an optimization approach. Four-point probe measurements are used as a reference. In addition, the spatial resistivity distribution is imaged by X-Y scanning of the samples to detect inhomogeneities in the doping distribution.

In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated through a small set of smooth functions. The invariance is either by translations under a full-rank lattice or through the action of crystallographic groups. Smoothness is ensured by stipulating that the generators belong to a Paley-Wiener space, that is selected in an optimal way based on the characteristics of the given data. To complete our investigation, we analyze the fundamental role played by the lattice in the process of approximation.

Given a mapping from a set of players to the leaves of a complete binary tree (called a seeding), a knockout tournament is conducted as follows: every round, every two players with a common parent compete against each other, and the winner is promoted to the common parent; then, the leaves are deleted. When only one player remains, it is declared the winner. This is a popular competition format in sports, elections, and decision-making. Over the past decade, it has been studied intensively from both theoretical and practical points of view. Most frequently, the objective is to seed the tournament in a way that "assists" (or even guarantees) some particular player to win the competition. We introduce a new objective, which is very sensible from the perspective of the directors of the competition: maximize the profit or popularity of the tournament. Specifically, we associate a "score" with every possible match, and aim to seed the tournament to maximize the sum of the scores of the matches that take place. We focus on the case where we assume a total order on the players' strengths, and provide a wide spectrum of results on the computational complexity of the problem.

We report the first near-infrared detection of Uranus's tiny moon Mab, the presumed source of the blue and diffuse $\mu$ ring, using the NIRC2 instrument at Keck Observatory. The detection was permitted by an updated shift-and-stack procedure allowing us to integrate on Mab as it moved across the detector in 23 separate exposures taken over $\sim$2 hours, as well as the very low (0.02$^{\circ}$) phase angle at the time of observation. At this phase angle, Mab has an integrated I/F of 24 $\pm$ 3 km$^2$ at 1.6 $\mu$m and $\lesssim$37 km$^2$ at 2.1 $\mu$m. Comparing these values with Mab's visible reflectance as derived by HST reveals that Mab is spectrally blue; its (0.5 $\mu$m)/(1.6 $\mu$m) color is more consistent with Miranda's value than Puck's value. Mab is therefore more likely a $\sim$6-km radius body with a Miranda-like surface than a 12-km radius body with a Puck-like surface, in agreement with prior work based on infrared upper limits, but we caution that a Puck-like color is only ruled out at the 2$\sigma$ level. We also report the first infrared photometry of Perdita, finding an integrated I/F of 31 $\pm$ 3 km$^2$ at 1.6 $\mu$m., Comment: 13 pages, 5 figures, published in Icarus Letters

Using archival near-infrared observations from the Keck and Lick Observatories and the Hubble Space Telescope, we document the evolution of Neptune's cloud activity from 1994 to 2022. We calculate the fraction of Neptune's disk that contained clouds, as well as the average brightness of both cloud features and cloud-free background over the planet's disk. We observe cloud activity and brightness maxima during 2002 and 2015, and minima during 2007 and 2020, the latter of which is particularly deep. Neptune's lack of cloud activity in 2020 is characterized by a near-total loss of clouds at mid-latitudes and continued activity at the South Pole. We find that the periodic variations in Neptune's disk-averaged brightness in the near-infrared H (1.6 $\mu$m), K (2.1 $\mu$m), FWCH4P15 (893 nm), F953N (955 nm), FWCH4P15 (965 nm), and F845M (845 nm) bands are dominated by discrete cloud activity, rather than changes in the background haze. The clear positive correlation we find between cloud activity and Solar Lyman-Alpha (121.56 nm) irradiance lends support to the theory that the periodicity in Neptune's cloud activity results from photochemical cloud/haze production triggered by Solar ultraviolet emissions., Comment: 46 pages, 13 figures, accepted to Icarus

Using near-infrared observations of Neptune from the Keck and Lick Observatories, and the Hubble Space Telescope in combination with amateur datasets, we calculated the drift rates of prominent infrared-bright cloud features on Neptune between 2018 and 2021. These features had lifespans of $\sim 1$ day to $\geq$1 month and were located at mid-latitudes and near the south pole. Our observations permitted determination of drift rates via feature tracking. These drift rates were compared to three zonal wind profiles describing Neptune's atmosphere determined from features tracked in H band (1.6 $\mu m$), K' band (2.1 $\mu m$), and Voyager 2 data at visible wavelengths. Features near $-70 \deg$ measured in the F845M filter (845nm) were particularly consistent with the K' wind profile. The southern mid-latitudes hosted multiple features whose lifespans were $\geq$1 month, providing evidence that these latitudes are a region of high stability in Neptune's atmosphere. We also used HST F467M (467nm) data to analyze a dark, circumpolar wave at $- 60 \deg$ latitude observed on Neptune since the Voyager 2 era. Its drift rate in recent years (2019-2021) is $4.866 \pm 0.009 \deg $/day. This is consistent with previous measurements by Karkoschka (2011), which predict a $4.858 \pm 0.022 \deg$/day drift rate during these years. It also gained a complementary bright band just to the north., Comment: 29 pages, 13 figures, accepted to Icarus

We present observations of Uranus in northern spring with the VLA from 0.7 cm to 5 cm. These observations reveal details in thermal emission from Uranus' north pole at 10s of bars, including a dark collar near 80N and a bright spot at the polar center. The bright central spot resembles observations of polar emission on Saturn and Neptune at shallower pressures. We constrain the variations in temperature and NH3/H2S abundances which could explain these features. We find that the brightness temperature of the polar spot can be recreated through 5 K temperature gradients and/or 10x depletion of NH3 or H2S vapor between 10-20 bars, both consistent with the presence of a cyclonic polar vortex. The contrast of the polar spot may have increased since 2015, which would suggest seasonal evolution of Uranus' polar circulation at depth., Comment: 14 pages, 4 figures, accepted to Geophysical Research Letters

Spintronic terahertz emitters promise terahertz sources with an unmatched broad frequency bandwidth that are easy to fabricate and operate, and therefore easy to scale at low cost. However, current experiments and proofs of concept rely on free-space ultrafast pump lasers and rather complex benchtop setups. This contrasts with the requirements of widespread industrial applications, where robust, compact, and safe designs are needed. To meet these requirements, we present a novel fiber-tip spintronic terahertz emitter solution that allows spintronic terahertz systems to be fully fiber-coupled. Using single-mode fiber waveguiding, the newly developed solution naturally leads to a simple and straightforward terahertz near-field imaging system with a 90%-10% knife-edge-response spatial resolution of 30 ${\mu}m$.

In this paper we initiate the study of the temporal graph realization problem with respect to the fastest path durations among its vertices, while we focus on periodic temporal graphs. Given an $n \times n$ matrix $D$ and a $\Delta \in \mathbb{N}$, the goal is to construct a $\Delta$-periodic temporal graph with $n$ vertices such that the duration of a fastest path from $v_i$ to $v_j$ is equal to $D_{i,j}$, or to decide that such a temporal graph does not exist. The variations of the problem on static graphs have been well studied and understood since the 1960's (e.g. [Erd\H{o}s and Gallai, 1960], [Hakimi and Yau, 1965]). As it turns out, the periodic temporal graph realization problem has a very different computational complexity behavior than its static (i.e. non-temporal) counterpart. First, we show that the problem is NP-hard in general, but polynomial-time solvable if the so-called underlying graph is a tree. Building upon those results, we investigate its parameterized computational complexity with respect to structural parameters of the underlying static graph which measure the ``tree-likeness''. We prove a tight classification between such parameters that allow fixed-parameter tractability (FPT) and those which imply W[1]-hardness. We show that our problem is W[1]-hard when parameterized by the feedback vertex number (and therefore also any smaller parameter such as treewidth, degeneracy, and cliquewidth) of the underlying graph, while we show that it is in FPT when parameterized by the feedback edge number (and therefore also any larger parameter such as maximum leaf number) of the underlying graph., Comment: 57 pages, 10 figures

A temporal graph has an edge set that may change over discrete time steps, and a temporal path (or walk) must traverse edges that appear at increasing time steps. Accordingly, two temporal paths (or walks) are temporally disjoint if they do not visit any vertex at the same time. The study of the computational complexity of finding temporally disjoint paths or walks in temporal graphs has recently been initiated by Klobas et al. [IJCAI '21]. This problem is motivated by applications in multi-agent path finding (MAPF), which include robotics, warehouse management, aircraft management, and traffic routing. We extend Klobas et al.'s research by providing parameterized hardness results for very restricted cases, with a focus on structural parameters of the so-called underlying graph. On the positive side, we identify sufficiently simple cases where we can solve the problem efficiently. Our results reveal some surprising differences between the "path version" and the "walk version" (where vertices may be visited multiple times) of the problem, and answer several open questions posed by Klobas et al.

Sugarcane production is a significant and profitable agribusiness sector in many countries. Nevertheless, this industry suffers significant losses from the sugarcane pests, among which the most important one is the sugarcane borer (Diatraea saccharalis). This pest population is hard to be controlled due to its different life stages, thus biological control (with more than one predator species) can be applied. Therefore, in this work, we present and analyze a mathematical model that describes the dynamics of the sugarcane borer and its two different life stages parasitoids: eggs (Trichogramma galloi}) and larval (Cotesia flavipes). First, a host-parasitoid model is used to obtain the population dynamics, which also considers the influence of seasonal variations. Then, system simulations and bifurcation diagrams show that the introduction of seasonality perturbations causes complex dynamics and results in limit cycles and strange attractors.

Sensing with undetected photons allows access to spectral regions with simultaneous detection of photons of another region and is based on nonlinear interferometry. To obtain the full information of a sample, the corresponding interferogram has to be analyzed in terms of amplitude and phase, which has been realized so far by multiple measurements followed by phase variation. Here, we present a polarization-optics-based phase-quadrature implementation in a nonlinear interferometer for imaging with undetected photons in the infrared region. This allows us to obtain phase and visibility with a single image acquisition without the need of varying optical paths or phases, thus enabling the detection of dynamic processes. We demonstrate the usefullness of our method on a static phase mask opaque to the detected photons as well as on dynamic measurement tasks as the drying of an isopropanol film and the stretching of an adhesive tape.

Terahertz time-domain spectroscopy systems based on resonator-internal repetition-rate modulation, such as SLAPCOPS [12] and ECOPS [11], rely on electronic phase detectors which are typically prone to exhibit both a non-negligible random and systematic timing error. This limits the quality of the recorded information significantly. Here, we present the results of our recent attempt to reduce these errors in our own electronic phase detection systems. A more than six-fold timing-jitter reduction from 59.0 fs to 8.6 fs led to a significant increase in both exploitable terahertz bandwidth and signal-to-noise ratio. Additionally, utilizing our interferometrically monitored delay line as a calibration standard, the systematic error could be removed almost entirely and thus, excellent resolution of spectral absorption lines be accomplished. These improvements increased the accuracy of our multi-layer thickness measurements based on electronic phase detection by more than a factor of five, pushing the overall performance well into the sub-{\mu}m regime., Comment: 11 pages, 8 figures

We provide new (parameterized) computational hardness results for Interval Scheduling on Unrelated Machines. It is a classical scheduling problem motivated from just-in-time or lean manufacturing, where the goal is to complete jobs exactly at their deadline. We are given $n$ jobs and $m$ machines. Each job has a deadline, a weight, and a processing time that may be different on each machine. The goal is find a schedule that maximized the total weight of jobs completed exactly at their deadline. Note that this uniquely defines a processing time interval for each job on each machine. Interval Scheduling on Unrelated Machines is closely related to coloring interval graphs and has been thoroughly studied for several decades. However, as pointed out by Mnich and van Bevern [Computers \& Operations Research, 2018], the parameterized complexity for the number $m$ of machines as a parameter remained open. We resolve this by showing that Interval Scheduling on Unrelated Machines is W[1]-hard when parameterized by the number $m$ of machines. To this end, we prove W[1]-hardness with respect to $m$ of the special case where we have parallel machines with eligible machine sets for jobs. This answers Open Problem 8 of Mnich and van Bevern's list of 15 open problems in the parameterized complexity of scheduling [Computers \& Operations Research, 2018]. Furthermore, we resolve the computational complexity status of the unweighted version of Interval Scheduling on Unrelated Machines by proving that it is NP-complete. This answers an open question by Sung and Vlach [Journal of Scheduling, 2005].

Let T be a bounded operator on a Hilbert space H, and F = {f_j: j in J} an at most countable set of vectors in H. In this note, we characterize the pairs {T, F} such that {T^n f: f in F, n in I} form a frame of H, for the cases of I = N_0 and I = Z. The characterization for unilateral iterations gives a similarity with the compression of the shift acting on model spaces of the Hardy space of analytic functions defined on the unit disk with values in $l^2(J). This generalizes recent work for iterations of a single function. In the case of bilateral iterations, the characterization is by the bilateral shift acting on doubly invariant subspaces of L^2(T,l^2(J)). Furthermore, we characterize the frames of iterations for vector-valued model operators when J is finite in terms of Toeplitz and multiplication operators in the unilateral and bilateral case, respectively. Finally, we study the problem of finding the minimal number of orbits that produce a frame in this context., Comment: 21 pages

The betweenness centrality of a vertex v is an important centrality measure that quantifies how many optimal paths between pairs of other vertices visit v. Computing betweenness centrality in a temporal graph, in which the edge set may change over discrete timesteps, requires us to count temporal paths that are optimal with respect to some criterion. For several natural notions of optimality, including foremost or fastest temporal paths, this counting problem reduces to #Temporal Path, the problem of counting all temporal paths between a fixed pair of vertices; like the problems of counting foremost and fastest temporal paths, #Temporal Path is #P-hard in general. Motivated by the many applications of this intractable problem, we initiate a systematic study of the prameterised and approximation complexity of #Temporal Path. We show that the problem presumably does not admit an FPT-algorithm for the feedback vertex number of the static underlying graph, and that it is hard to approximate in general. On the positive side, we proved several exact and approximate FPT-algorithms for special cases.

The $1 \mid \mid \Sigma w_j U_j$ problem asks to determine -- given $n$ jobs each with its own processing time, weight, and due date -- the minimum weighted number of tardy jobs in any single machine non-preemptive schedule for these jobs. This is a classical scheduling problem that generalizes both Knapsack, and Subset Sum. The best known pseudo-polynomial algorithm for $1 \mid \mid \Sigma w_j U_j$, due to Lawler and Moore [Management Science'69], dates back to the late 60s and has a running time of $O(d_{\max}n)$, where $n$ is the number of jobs and $d_{\max}$ is their maximal due date. A recent lower bound by Cygan \emph{et al.}~[ICALP'19] for Knapsack shows that $1 \mid \mid \Sigma w_j U_j$ cannot be solved in $\widetilde{O}((n+d_{\max})^{2-\varepsilon})$ time, for any $\varepsilon > 0$, under a plausible conjecture. This still leaves a gap between the best known lower bound and upper bound for the problem. In this paper we design a new simple algorithm for $1 \mid \mid \Sigma w_j U_j$ that uses $(\max,+)$-convolutions as its main tool, and outperforms the Lawler and Moore algorithm under several parameter ranges. In particular, depending on the specific method of computing $(\max,+)$-convolutions, its running time can be bounded by - $\widetilde{O}(n+d_{\#}d_{\max}^2)$. - $\widetilde{O}(d_{\#}n +d^2_{\#}d_{\max}w_{\max})$. - $\widetilde{O}(d_{\#}n +d_{\#}d_{\max}p_{\max})$. - $\widetilde{O}(n^2 +d_{\max}w^2_{\max})$. - $\widetilde{O}(n^2 + d_{\#}(d_{\max}w_{\max})^{1.5})$. Here, $d_{\#}$ denotes the number of \emph{different} due dates in the instance, $p_{\max}$ denotes the maximum processing time of any job, and $w_{\max}$ denotes the maximum weight of any job.

A graph is temporally connected if there exists a strict temporal path, i.e. a path whose edges have strictly increasing labels, from every vertex $u$ to every other vertex $v$. In this paper we study temporal design problems for undirected temporally connected graphs. The basic setting of these optimization problems is as follows: given a connected undirected graph $G$, what is the smallest number $|\lambda|$ of time-labels that we need to add to the edges of $G$ such that the resulting temporal graph $(G,\lambda)$ is temporally connected? As it turns out, this basic problem, called MINIMUM LABELING (ML), can be optimally solved in polynomial time. However, exploiting the temporal dimension, the problem becomes more interesting and meaningful in its following variations, which we investigate in this paper. First we consider the problem MIN. AGED LABELING (MAL) of temporally connecting the graph when we are given an upper-bound on the allowed age (i.e. maximum label) of the obtained temporal graph $(G,\lambda)$. Second we consider the problem MIN. STEINER LABELING (MSL), where the aim is now to have a temporal path between any pair of "terminals" vertices which lie in a subset $R\subseteq V$. This relaxed problem resembles STEINER TREE in static graphs. However, due to the requirement of strictly increasing labels in a temporal path, STEINER TREE is not a special case of MSL. Finally we consider the age-restricted version of MSL, namely MIN. AGED STEINER LABELING (MASL). Our main results are threefold: we prove that (i) MAL becomes NP-complete on undirected graphs, while (ii) MASL becomes W[1]-hard with respect to the number $|R|$ of terminals. On the other hand we prove that (iii) although the age-unrestricted problem MSL is NP-hard, it is in FPT with respect to the number $|R|$ of terminals. That is, adding the age restriction, makes the above problems strictly harder., Comment: 45 pages, 36 figures

Nonlinear frequency conversion provides an elegant method to detect photons in a spectral range which differs from the pump wavelength, making it highly attractive for photons with inherently low energy. Aside from the intensity of the light, represented by the number of photons, their phase provides important information and enables a plethora of applications. We present a phase-sensitive measurement method in the terahertz spectral range by only detecting visible light. Using the optical interference of frequency-converted photons and leftover pump photons of the involved ultrashort pulses, fast determination of layer-thicknesses is demonstrated. The new method enables phase-resolved detection of terahertz pulses using standard sCMOS equipment while achieving sample measurement times of less than one second with a precision error of less than 0.6%., Comment: 10 pages, 5 figures

Most transportation networks are inherently temporal: Connections (e.g. flights, train runs) are only available at certain, scheduled times. When transporting passengers or commodities, this fact must be considered for the the planning of itineraries. This has already led to several well-studied algorithmic problems on temporal graphs. The difficulty of the described task is increased by the fact that connections are often unreliable -- in particular, many modes of transportation suffer from occasional delays. If these delays cause subsequent connections to be missed, the consequences can be severe. Thus, it is a vital problem to design itineraries that are robust to (small) delays. We initiate the study of this problem from a parameterized complexity perspective by proving its NP-completeness as well as several hardness and tractability results for natural parameterizations.

Consider planning a trip in a train network. In contrast to, say, a road network, the edges are temporal, i.e., they are only available at certain times. Another important difficulty is that trains, unfortunately, sometimes get delayed. This is especially bad if it causes one to miss subsequent trains. The best way to prepare against this is to have a connection that is robust to some number of (small) delays. An important factor in determining the robustness of a connection is how far in advance delays are announced. We give polynomial-time algorithms for the two extreme cases: delays known before departure and delays occurring without prior warning (the latter leading to a two-player game scenario). Interestingly, in the latter case, we show that the problem becomes PSPACE-complete if the itinerary is demanded to be a path.

The Internet of Things (IoT) is a paradigm characterized by a network of embedded sensors and services. These sensors are incorporated to collect various information, track physical conditions, e.g., waste bins' status, and exchange data with different centralized platforms. The need for such sensors is increasing; however, proliferation of technologies comes with various challenges. For example, how can IoT and its associated data be used to enhance waste management? In smart cities, an efficient waste management system is crucial. Artificial Intelligence (AI) and IoT-enabled approaches can empower cities to manage the waste collection. This work proposes an intelligent approach to route recommendation in an IoT-enabled waste management system given spatial constraints. It performs a thorough analysis based on AI-based methods and compares their corresponding results. Our solution is based on a multiple-level decision-making process in which bins' status and coordinates are taken into account to address the routing problem. Such AI-based models can help engineers design a sustainable infrastructure system., Comment: 11

Recent research found that fairness plays a key role in customer satisfaction. Therefore, many manufacturing and services industries have become aware of the need to treat customers fairly. Still, there is a huge lack of models that enable industries to make operational decisions fairly, such as a fair scheduling of the customers' jobs. Our main aim in this research is to provide a unified framework to enable schedulers making fair decisions in repetitive scheduling environments. For doing so, we consider a set of repetitive scheduling problems involving a set of $n$ clients. In each out of $q$ consecutive operational periods (e.g. days), each one of the customers submits a job for processing by an operational system. The scheduler's aim is to provide a schedule for each of the $q$ periods such that the quality of service (QoS) received by each of the clients will meet a certain predefined threshold. The QoS of a client may take several different forms, e.g., the number of days that the customer receives its job later than a given due-date, the number of times the customer receive his preferred time slot for service, or the sum of waiting times for service. We analyze the single machine variant of the problem for several different definitions of QoS, and classify the complexity of the corresponding problems using the theories of classical and parameterized complexity. We also study the price of fairness, i.e., the loss in the system's efficiency that results from the need to provide fair solutions.

Spontaneous parametric down-conversion (SPDC) sources are an important technology for quantum sensing and imaging. We demonstrate a general simulation method, based on modeling from first principles, reproducing the spectrally and spatially resolved absolute counts of a SPDC experiment. By simulating additional processes and effects we accomplish good agreement with the experimental results. This method is broadly applicable and allows for the separation of contributing processes, virtual characterization of SPDC sources, and enables the simulation of many quantum based applications., Comment: 6 pages, 4 figures; changed style; extended discussion in section 3

Temporal graphs have been recently introduced to model changes to a given network that occur throughout a fixed period of time. The Temporal $\Delta$ Clique problem, that generalizes the well known Clique problem to temporal graphs, has been studied in the context of finding nodes of interest in dynamic networks [TCS '16]. We introduce the Temporal $\Delta$ Independent Set problem, a temporal generalization of Independent Set. This problem is e.g. motivated in the context of finding conflict-free schedules for maximum subsets of tasks, that have certain (changing) constraints on each day they need to be performed. We are specifically interested in the case where each task needs to be performed in a certain time-interval on each day and two tasks are in conflict on a certain day if their time-intervals on that day overlap. This leads us to considering both problems on the restricted class of temporal unit interval graphs, i.e., temporal graphs where each layer is a unit interval graph. We present several hardness results as well as positive results. On the algorithmic side, we provide constant-factor approximation algorithms for instances of both problems where $\tau$, the total number of time steps (layers) of the temporal graph, and $\Delta$, a parameter that allows us to model conflict tolerance, are constants. We develop an exact FPT algorithm for Temporal $\Delta$ Clique with respect to parameter $\tau+k$. Finally, we use the notion of order preservation for temporal unit interval graphs that, informally, requires the intervals of every layer to obey a common ordering. For both problems we provide an FPT algorithm parameterized by the size of minimum vertex deletion set to order preservation.