Embedded real-time systems must meet timing constraints while minimizing energy consumption. To this end, many energy optimizations are introduced for specific platforms or specific applications. These solutions are not portable, however, and when the application or the platform change, these solutions must be redesigned. Portable techniques are hard to develop due to the varying tradeoffs experienced with different application/platform configurations. This paper addresses the problem of finding and exploiting general tradeoffs, using control theory and mathematical optimization to achieve energy minimization under soft real-time application constraints. The paper presents POET, an open-source C library and runtime system that takes a specification of the platform resources and optimizes the application execution. We test POET's ability to portably deliver predictable timing and energy reduction on two embedded systems with different tradeoff spaces -the first with a mobile Intel Haswell processor, and the second with an ARM big.LITTLE System on Chip. POET achieves the desired latency goals with small error while consuming, on average, only 1.3% more energy than the dynamic optimal oracle on the Haswell and 2.9% more on the ARM. We believe this open-source, librarybased approach to resource management will simplify the process of writing portable, energy-efficient code for embedded systems.

BackgroundCerebral amyloid angiopathy (CAA) is characterized by deposition of fibrillar amyloid β (Aβ) within cerebral vessels. It is commonly seen in the elderly and almost universally present in patients with Alzheimer's Disease (AD). In both patient populations, CAA is an independent risk factor for lobar hemorrhage, ischemic stroke, and dementia. To date, definitive diagnosis of CAA requires obtaining pathological tissues via brain biopsy (which is rarely clinically indicated) or at autopsy. Though amyloid tracers labeled with positron-emitting radioligands such as [11C]PIB have shown promise for non-invasive amyloid imaging in AD patients, to date they have been unable to clarify whether the observed amyloid load represents neuritic plaques versus CAA due in large part to the low resolution of PET imaging and the almost equal affinity of these tracers for both vascular and parenchymal amyloid. Therefore, the development of a precise and specific non-invasive technique for diagnosing CAA in live patients is desired.ResultsWe found that the phenoxazine derivative resorufin preferentially bound cerebrovascular amyloid deposits over neuritic plaques in the aged Tg2576 transgenic mouse model of AD/CAA, whereas the congophilic amyloid dye methoxy-X34 bound both cerebrovascular amyloid deposits and neuritic plaques. Similarly, resorufin-positive staining was predominantly noted in fibrillar Aβ-laden vessels in postmortem AD brain tissues. Fluorescent labeling and multi-photon microscopy further revealed that both resorufin- and methoxy-X34-positive staining is colocalized to the vascular smooth muscle (VSMC) layer of vessel segments that have severe disruption of VSMC arrangement, a characteristic feature of CAA. Resorufin also selectively visualized vascular amyloid deposits in live Tg2576 mice when administered topically, though not systemically. Resorufin derivatives with chemical modification at the 7-OH position of resorufin also displayed a marked preferential binding affinity for CAA, but with enhanced lipid solubility that indicates their use as a non-invasive imaging tracer for CAA is feasible.ConclusionsTo our knowledge, resorufin analogs are the fist class of amyloid dye that can discriminate between cerebrovascular and neuritic forms of amyloid. This unique binding selectivity suggests that this class of dye has great potential as a CAA-specific amyloid tracer that will permit non-invasive detection and quantification of CAA in live patients.

We study the classical Node-Disjoint Paths (NDP) problem: given an undirected n-vertex graph G, together with a set {(s 1 , t 1 ), . . . , (s k , t k )} of pairs of its vertices, called source-destination, or demand pairs, find a maximum-cardinality set P of mutually node-disjoint paths that connect the demand pairs. The best current approximation for the problem is achieved by a simple greedy O( √ n)-approximation algorithm. Until recently, the best negative result was an Ω(log 1/2− n)hardness of approximation, for any fixed , under standard complexity assumptions. A special case of the problem, where the underlying graph is a grid, has been studied extensively. The best current approximation algorithm for this special case achieves anÕ(n 1/4 )-approximation factor. On the negative side, a recent result by the authors shows that NDP is hard to approximate to within factor 2 Ω( * Toyota Technological Institute at Chicago.In this paper we explore NDP-Grid. This important special case of NDP was initially motivated by applications in VLSI design, and has received a lot of attention since the 1960's. We focus on a restricted version of NDP-Grid, that we call Restricted NDP-Grid: here, in addition to the graph G being a square grid, we also require that all source vertices {s 1 , . . . , s k } lie on the grid boundary. We do not make any assumptions about the locations of the destination vertices, that may appear anywhere in the grid. The best current approximation algorithm for Restricted NDP-Grid is the same as that for the general NDP-Grid, and achieves aÕ(n 1/4 )-approximation [CK15]. Our main result is summarized in the following theorem.This result in a sense complements the 2 Ω( √ log n) -hardness of approximation of NDP on sub-graphs of grids with all sources lying on the grid boundary of [CKN17] 2 , and should be contrasted with the recent almost polynomial hardness of approximation of [CKN18] for NDP-Grid mentioned above. Our algorithm departs from previous work on NDP in that it does not use the multicommodity flow relaxation. Instead, we define sufficient conditions that allow us to route a subset M of demand pairs via disjoint paths, and show that there exists a subset of demand pairs satisfying these conditions, whose cardinality is at least OPT/2 O( √ log n·log log n) , where OPT is the value of the optimal solution. It is then enough to compute a maximum-cardinality subset of the demand pairs satisfying these conditions. We write an LP-relaxation for this problem and design a 2 O( √ log n·log log n) -approximation LP-rounding algorithm for it. We emphasize that the linear program is only used to select the demand pairs to be routed, and not to compute the routing itself.We then generalize the result to instances where the source vertices lie within a prescribed distance from the grid boundary.Theorem 1.2 For every integer δ ≥ 1, there is an efficient randomized δ · 2 O( √ log n·log log n) -approximation algorithm for the special case of NDP-Grid where all source vertices lie within distance at most δ ...

In the classical Node-Disjoint Paths (NDP) problem, the input consists of an undirected nvertex graph G, and a collection M = {(s 1 , t 1 ), . . . , (s k , t k )} of pairs of its vertices, called sourcedestination, or demand, pairs. The goal is to route the largest possible number of the demand pairs via node-disjoint paths. The best current approximation for the problem is achieved by a simple greedy algorithm, whose approximation factor is O( √ n), while the best current negative result is an Ω(log 1/2−δ n)-hardness of approximation for any constant δ, under standard complexity assumptions. Even seemingly simple special cases of the problem are still poorly understood: when the input graph is a grid, the best current algorithm achieves anÕ(n 1/4 )-approximation, and when it is a general planar graph, the best current approximation ratio of an efficient algorithm isÕ(n 9/19 ). The best currently known lower bound on the approximability of both these versions of the problem is APX-hardness.In this paper we prove that NDP is 2 Ω( √ log n) -hard to approximate, unless all problems in NP have algorithms with running time n O(log n) . Our result holds even when the underlying graph is a planar graph with maximum vertex degree 3, and all source vertices lie on the boundary of a single face (but the destination vertices may lie anywhere in the graph). We extend this result to the closely related Edge-Disjoint Paths problem, showing the same hardness of approximation ratio even for sub-cubic planar graphs with all sources lying on the boundary of a single face.

We study the Node-Disjoint Paths (NDP) problem: given an undirected n-vertex graph G and a collection M = {(s 1 , t 1 ), . . . , (s k , t k )} of pairs of its vertices, called source-destination, or demand pairs, we are interested in routing the demand pairs, where in order to route a pair (s i , t i ), we need to select a path connecting s i to t i . The goal is to route as many of the pairs as possible, subject to the constraint that the selected routing paths are mutually disjoint in their vertices and their edges. We let S = {s 1 , . . . , s k } be the set of the source vertices, T = {t 1 , . . . , t k } the set of the destination vertices, and we refer to the vertices of S ∪ T as terminals. We denote by NDP-Planar the special case of the problem where the graph G is planar; by NDP-Grid the special case where G is a square grid; and by NDP-Wall the special case where G is a wall (see Figure 1 for an illustration of a wall and Section 2 for its formal definition).NDP is a fundamental problem in the area of graph routing, that has been studied extensively. Robertson and Seymour [RS90, RS95] showed, as part of their famous Graph Minors Series, an efficient algorithm for solving the problem if the number k of the demand pairs is bounded by a constant. However, when k is a part of the input, the problem becomes NP-hard [Kar75, EIS76], and it remains NP-hard even for planar graphs [Lyn75], and for grid graphs [KvL84]. The best current upper bound on the approximability of NDP is O( √ n), obtained by a simple greedy algorithm [KS04]. Until recently, the best known lower bound was an Ω(log 1/2− n)-hardness of approximation for any constant , unless NP ⊆ ZPTIME(n poly log n ) [AZ05, ACG + 10], and APX-hardness for the special cases of NDP-Planar and NDP-Grid [CK15]. In a recent paper [CKN17b], the authors have shown an improved 2 Ω( √ log n)hardness of approximation for NDP, assuming that NP DTIME(n O(log n) ). This result holds even for planar graphs with maximum vertex degree 3, where all source vertices lie on the boundary of a single face, and for sub-graphs of grid graphs, with all source vertices lying on the boundary of the grid. We note that for general planar graphs, the O( √ n)-approximation algorithm of [KS04] was recently slightly improved to anÕ(n 9/19 )-approximation [CKL16].The approximability status of NDP-Gridthe special case of NDP where the underlying graph is a square grid -remained a tantalizing open question. The study of this problem dates back to the 70's, and was initially motivated by applications to VLSI design. As grid graphs are extremely wellstructured, one would expect that good approximation algorithms can be designed for them, or that, at the very least, they should be easy to understand. However, establishing the approximability of NDP-Grid has been elusive so far. The simple greedy O( √ n)-approximation algorithm of [KS04] was only recently improved to aÕ(n 1/4 )-approximation for NDP-Grid [CK15], while on the negative side only APX-hardness is known. In a very recent paper [CKN17a],...