Multiple-interval graphs are a natural generalization of interval graphs where each vertex may have more than one interval associated with it. Many applications of interval graphs also generalize to ...multiple-interval graphs, often allowing for more robustness in the modeling of the specific application. With this motivation in mind, a recent systematic study of optimization problems in multiple-interval graphs was initiated. In this sequel, we study multiple-interval graph problems from the perspective of parameterized complexity. The problems under consideration are
k
-
Independent Set,
k
-
Dominating Set, and
k
-
Clique, which are all known to be W1-hard for general graphs, and NP-complete for multiple-interval graphs. We prove that
k
-
Clique is in FPT, while
k
-
Independent Set and
k
-
Dominating Set are both W1-hard. We also prove that
k
-
Independent Dominating Set, a hybrid of the two above problems, is also W1-hard. Our hardness results hold even when each vertex is associated with at most two intervals, and all intervals have unit length. Furthermore, as an interesting byproduct of our hardness results, we develop a useful technique for showing W1-hardness via a reduction from the
k
-
Multicolored Clique problem, a variant of
k
-
Clique. We believe this technique has interest in its own right, as it should help in simplifying W1-hardness results which are notoriously hard to construct and technically tedious.
Current cell-based repair strategies have proven unsuccessful for treating cartilage defects and osteoarthritic lesions, consequently advances in innovative therapeutics are required and mesenchymal ...stem cell-based (MSC) therapies are an expanding area of investigation. MSCs are capable of differentiating into multiple cell lineages and exerting paracrine effects. Due to their easy isolation, expansion, and low immunogenicity, MSCs are an attractive option for regenerative medicine for joint repair. Recent studies have identified several MSC tissue reservoirs including in adipose tissue, bone marrow, cartilage, periosteum, and muscle. MSCs isolated from these discrete tissue niches exhibit distinct biological activities, and have enhanced regenerative potentials for different tissue types. Each MSC type has advantages and disadvantages for cartilage repair and their use in a clinical setting is a balance between expediency and effectiveness. In this review we explore the challenges associated with cartilage repair and regeneration using MSC-based cell therapies and provide an overview of phenotype, biological activities, and functional properties for each MSC population. This paper also specifically explores the therapeutic potential of each type of MSC, particularly focusing on which cells are capable of producing stratified hyaline-like articular cartilage regeneration. Finally we highlight areas for future investigation. Given that patients present with a variety of problems it is unlikely that cartilage regeneration will be a simple "one size fits all," but more likely an array of solutions that need to be applied systematically to achieve regeneration of a biomechanically competent repair tissue.
Multiple factors simultaneously affect the spiking activity of individual neurons. Determining the effects and relative importance of these factors is a challenging problem in neurophysiology. We ...propose a statistical framework based on the point process likelihood function to relate a neuron's spiking probability to three typical covariates: the neuron's own spiking history, concurrent ensemble activity, and extrinsic covariates such as stimuli or behavior. The framework uses parametric models of the conditional intensity function to define a neuron's spiking probability in terms of the covariates. The discrete time likelihood function for point processes is used to carry out model fitting and model analysis. We show that, by modeling the logarithm of the conditional intensity function as a linear combination of functions of the covariates, the discrete time point process likelihood function is readily analyzed in the generalized linear model (GLM) framework. We illustrate our approach for both GLM and non-GLM likelihood functions using simulated data and multivariate single-unit activity data simultaneously recorded from the motor cortex of a monkey performing a visuomotor pursuit-tracking task. The point process framework provides a flexible, computationally efficient approach for maximum likelihood estimation, goodness-of-fit assessment, residual analysis, model selection, and neural decoding. The framework thus allows for the formulation and analysis of point process models of neural spiking activity that readily capture the simultaneous effects of multiple covariates and enables the assessment of their relative importance.
Pain places a devastating burden on patients and society and current pain therapeutics exhibit limitations in efficacy, unwanted side effects and the potential for drug abuse and diversion. Although ...genetic evidence has clearly demonstrated that the voltage-gated sodium channel, Nav1.7, is critical to pain sensation in mammals, pharmacological inhibitors of Nav1.7 have not yet fully recapitulated the dramatic analgesia observed in Nav1.7-null subjects. Using the tarantula venom-peptide ProTX-II as a scaffold, we engineered a library of over 1500 venom-derived peptides and identified JNJ63955918 as a potent, highly selective, closed-state Nav1.7 blocking peptide. Here we show that JNJ63955918 induces a pharmacological insensitivity to pain that closely recapitulates key features of the Nav1.7-null phenotype seen in mice and humans. Our findings demonstrate that a high degree of selectivity, coupled with a closed-state dependent mechanism of action is required for strong efficacy and indicate that peptides such as JNJ63955918 and other suitably optimized Nav1.7 inhibitors may represent viable non-opioid alternatives for the pharmacological treatment of severe pain.
A pursuit-tracking task (PTT) and multielectrode recordings were used to investigate the spatiotemporal encoding of hand position and velocity in primate primary motor cortex (MI). Continuous ...tracking of a randomly moving visual stimulus provided a broad sample of velocity and position space, reduced statistical dependencies between kinematic variables, and minimized the nonstationarities that are found in typical "step-tracking" tasks. These statistical features permitted the application of signal-processing and information-theoretic tools for the analysis of neural encoding. The multielectrode method allowed for the comparison of tuning functions among simultaneously recorded cells. During tracking, MI neurons showed heterogeneity of position and velocity coding, with markedly different temporal dynamics for each. Velocity-tuned neurons were approximately sinusoidally tuned for direction, with linear speed scaling; other cells showed sinusoidal tuning for position, with linear scaling by distance. Velocity encoding led behavior by about 100 ms for most cells, whereas position tuning was more broadly distributed, with leads and lags suggestive of both feedforward and feedback coding. Individual cells encoded velocity and position weakly, with comparable amounts of information about each. Linear regression methods confirmed that random, 2-D hand trajectories can be reconstructed from the firing of small ensembles of randomly selected neurons (3-19 cells) within the MI arm area. These findings demonstrate that MI carries information about evolving hand trajectory during visually guided pursuit tracking, including information about arm position both during and after its specification. However, the reconstruction methods used here capture only the low-frequency components of movement during the PTT. Hand motion signals appear to be represented as a distributed code in which diverse information about position and velocity is available within small regions of MI.
Multiple-electrode arrays are valuable both as a research tool and as a sensor for neuromotor prosthetic devices, which could potentially restore voluntary motion and functional independence to ...paralyzed humans. Long-term array reliability is an important requirement for these applications. Here, we demonstrate the reliability of a regular array of 100 microelectrodes to obtain neural recordings from primary motor cortex (MI) of monkeys for at least three months and up to 1.5 years. We implanted Bionic (Cyberkinetics, Inc., Foxboro, MA) silicon probe arrays in MI of three Macaque monkeys. Neural signals were recorded during performance of an eight-direction, push-button task. Recording reliability was evaluated for 18, 35, or 51 sessions distributed over 83, 179, and 569 days after implantation, respectively, using qualitative and quantitative measures. A four-point signal quality scale was defined based on the waveform amplitude relative to noise. A single observer applied this scale to score signal quality for each electrode. A mean of 120 (/spl plusmn/17.6 SD), 146 (/spl plusmn/7.3), and 119 (/spl plusmn/16.9) neural-like waveforms were observed from 65-85 electrodes across subjects for all recording sessions of which over 80% were of high quality. Quantitative measures demonstrated that waveforms had signal-to-noise ratio (SNR) up to 20 with maximum peak-to-peak amplitude of over 1200 /spl mu/v with a mean SNR of 4.8 for signals ranked as high quality. Mean signal quality did not change over the duration of the evaluation period (slope 0.001, 0.0068 and 0.03; NS). By contrast, neural waveform shape varied between, but not within days in all animals, suggesting a shifting population of recorded neurons over time. Arm-movement related modulation was common and 66% of all recorded neurons were tuned to reach direction. The ability for the array to record neural signals from parietal cortex was also established. These results demonstrate that neural recordings that can provide movement related signals for neural prostheses, as well as for fundamental research applications, can be reliably obtained for long time periods using a monolithic microelectrode array in primate MI and potentially from other cortical areas as well.
•Electoral control models ways of changing the outcome of an election via adding, deleting, or partitioning candidates or voters.•A long-running project of research seeks to classify the major voting ...systems in terms of their computational resistance.•We show that fallback voting is resistant to each of the common types of control except two destructive control types.•We show that Bucklin voting performs almost as well as fallback voting in terms of control resistance.•We investigate the parameterized control complexity of Bucklin and fallback voting.
Electoral control models ways of changing the outcome of an election via such actions as adding, deleting, or partitioning either candidates or voters. To protect elections from such control attempts, computational complexity has been used to establish so-called resistance results. We show that fallback voting, an election system proposed by Brams and Sanver 12 to combine Bucklin with approval voting, displays the broadest control resistance currently known to hold among natural election systems with a polynomial-time winner problem. We also study the control complexity of Bucklin voting and show that it performs almost as well as fallback voting in terms of control resistance. Furthermore, we investigate the parameterized control complexity of Bucklin and fallback voting, according to several parameters that are often likely to be small for typical instances. In a companion paper 28, we challenge our worst-case complexity results from an experimental point of view.
Instant neural control of a movement signal SERRUYA, Mijail D; HATSOPOULOS, Nicholas G; PANINSKI, Liam ...
Nature (London),
03/2002, Letnik:
416, Številka:
6877
Journal Article
Recenzirano
The activity of motor cortex (MI) neurons conveys movement intent sufficiently well to be used as a control signal to operate artificial devices, but until now this has called for extensive training ...or has been confined to a limited movement repertoire. Here we show how activity from a few (7-30) MI neurons can be decoded into a signal that a monkey is able to use immediately to move a computer cursor to any new position in its workspace (14 degrees x 14 degrees visual angle). Our results, which are based on recordings made by an electrode array that is suitable for human use, indicate that neurally based control of movement may eventually be feasible in paralysed humans.
In this paper, we study the complexity of several coloring problems on graphs, parameterized by the treewidth of the graph.
1.
The
List Coloring problem takes as input a graph
G, together with an ...assignment to each vertex
v of a set of colors
C
v
. The problem is to determine whether it is possible to choose a color for vertex
v from the set of permitted colors
C
v
, for each vertex, so that the obtained coloring of
G is proper. We show that this problem is
W
1
-hard, parameterized by the treewidth of
G. The closely related
Precoloring Extension problem is also shown to be
W
1
-hard, parameterized by treewidth.
2.
An
equitable coloring of a graph
G is a proper coloring of the vertices where the numbers of vertices having any two distinct colors differs by at most one. We show that the problem is hard for
W
1
, parameterized by the treewidth plus the number of colors. We also show that a list-based variation,
List Equitable Coloring is
W
1
-hard for forests, parameterized by the number of colors on the lists.
3.
The
list chromatic number
χ
l
(
G
)
of a graph
G is defined to be the smallest positive integer
r, such that for every assignment to the vertices
v of
G, of a list
L
v
of colors, where each list has length at least
r, there is a choice of one color from each vertex list
L
v
yielding a proper coloring of
G. We show that the problem of determining whether
χ
l
(
G
)
⩽
r
, the
List Chromatic Number problem, is solvable in linear time on graphs of constant treewidth.
Sensory processing in the brain includes three key operations: multisensory integration-the task of combining cues into a single estimate of a common underlying stimulus; coordinate ...transformations-the change of reference frame for a stimulus (e.g., retinotopic to body-centered) effected through knowledge about an intervening variable (e.g., gaze position); and the incorporation of prior information. Statistically optimal sensory processing requires that each of these operations maintains the correct posterior distribution over the stimulus. Elements of this optimality have been demonstrated in many behavioral contexts in humans and other animals, suggesting that the neural computations are indeed optimal. That the relationships between sensory modalities are complex and plastic further suggests that these computations are learned-but how? We provide a principled answer, by treating the acquisition of these mappings as a case of density estimation, a well-studied problem in machine learning and statistics, in which the distribution of observed data is modeled in terms of a set of fixed parameters and a set of latent variables. In our case, the observed data are unisensory-population activities, the fixed parameters are synaptic connections, and the latent variables are multisensory-population activities. In particular, we train a restricted Boltzmann machine with the biologically plausible contrastive-divergence rule to learn a range of neural computations not previously demonstrated under a single approach: optimal integration; encoding of priors; hierarchical integration of cues; learning when not to integrate; and coordinate transformation. The model makes testable predictions about the nature of multisensory representations.
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