Higher rank numerical ranges of normal matrices

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix $A \in M_n$ has eigenvalues $a_1, \..., a_n$, then its higher rank numerical range $\Lambda_k(A)$ is the intersection of convex polygons with vertices $a_{j_1}, \..., a_{j_{n-k+1}}$, where $1 \le j_1 < \... < j_{n-k+1} \le n$. In this paper, it is shown that the higher rank numerical range of a normal matrix with $m$ distinct eigenvalues can be written as the intersection of no more than $\max\{m,4\}$ closed half planes. In addition, given a convex polygon ${\mathcal P}$ a construction is given for a normal matrix $A \in M_n$ with minimum $n$ such that $\Lambda_k(A) = {\mathcal P}$. In particular, if ${\mathcal P}$ has $p$ vertices, with $p \ge 3$, there is a normal matrix $A \in M_n$ with $n \le \max\left\{p+k-1, 2k+2 \right\}$ such that $\Lambda_k(A) = {\mathcal P}$.Comment: 12 pages, 9 figures, to appear in SIAM Journal on Matrix Analysis and Application

Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace

When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free subspace are known to correct such collective errors. We construct simple quantum circuits, which implement these collective error correction codes, for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and $n=4$, while two logical qubits are encoded with $n=5$. The recursive relations among the subspaces employed in noiseless subsystem and decoherence free subspace play essential r\^oles in our implementation. The recursive relations also show that the number of gates required to encode $m$ logical qubits increases linearly in $m$.Comment: 9 pages, 3 figure

A note on the realignment criterion

For a quantum state in a bipartite system represented as a density matrix, researchers used the realignment matrix and functions on its singular values to study the separability of the quantum state. We obtain bounds for elementary symmetric functions of singular values of realignment matrices. This answers some open problems proposed by Lupo, Aniello, and Scardicchio. As a consequence, we show that the proposed scheme by these authors for testing separability would not work if the two subsystems of the bipartite system have the same dimension.Comment: 11 pages, to appear in Journal of Physics A: Mathematical and Theoretica

Preliminary results of trial NPC-0501 evaluating the therapeutic gain by changing from concurrent-adjuvant to induction-concurrent chemoradiotherapy, changing from fluorouracil to capecitabine, and changing from conventional to accelerated radiotherapy fractionation in patients with locoregionally advanced nasopharyngeal carcinoma

© 2014 American Cancer Society. BACKGROUND A current recommendation for locoregionally advanced nasopharyngeal carcinoma (NPC) is conventional fractionated radiotherapy with concurrent cisplatin plus adjuvant cisplatin and fluorouracil (PF). In this randomized trial, the authors evaluated the potential therapeutic benefit from changing to an induction-concurrent chemotherapy sequence, replacing fluorouracil with oral capecitabine, and/or using accelerated rather than conventional radiotherapy fractionation. METHODS Patients with stage III through IVB, nonkeratinizing NPC were randomly allocated to 1 of 6 treatment arms. The protocol was amended in 2009 to permit confining randomization to the conventional fractionation arms. The primary endpoint was progression-free survival. Secondary endpoints included overall survival and safety. RESULTS In total, 803 patients were accrued, and 706 patients were randomly allocated to all 6 treatment arms. Comparisons of induction PF versus adjuvant PF did not indicate a significant improvement. Unadjusted comparisons of induction cisplatin and capecitabine (PX) versus adjuvant PF indicated a favorable trend in progression-free survival for the conventional fractionation arm (P = .045); analyses that were adjusted for other significant factors and fractionation reflected a significant reduction in the hazards of disease progression (hazard ratio [HR], 0.54; 95% confidence interval [CI], 0.36-0.80) and death (HR, 0.42; 95% CI, 0.25-0.70). Unadjusted comparisons of induction sequences versus adjuvant sequences did not reach statistical significance, but adjusted comparisons indicated favorable improvements by induction sequence. Comparisons of induction PX versus induction PF revealed fewer toxicities (neutropenia and electrolyte disturbance), unadjusted comparisons of efficacy were statistically insignificant, but adjusted analyses indicated that induction PX had a lower hazard of death (HR, 0.57; 95% CI, 0.34-0.97). Changing the fractionation from conventional to accelerated did not achieve any benefit but incurred higher toxicities (acute mucositis and dehydration). CONCLUSIONS Preliminary results indicate that the benefit of changing to an induction-concurrent sequence remains uncertain; replacing fluorouracil with oral capecitabine warrants further validation in view of its convenience, favorable toxicity profile, and favorable trends in efficacy; and accelerated fractionation is not recommended for patients with locoregionally advanced NPC who receive chemoradiotherapy.postprin

Effects of physical activity on functional health of older adults: a systematic review

Reviews on the relationships between functional health and physical activity of general older adults have been well documented in literature. However, specific age range of older adults, in particular, older adults of 75 years or above, is currently under-examined. A systematic review was conducted to investigate the effects of physical activity on functional health older adults aged 75 years or above. The reviewed articles cover a variety range of functional health outcomes, including balance, muscle conditioning, joint range of motion, quadriceps strength, reaction time, gait speed, health-related quality of life, back and knee pain, muscle mass, and walking ability. In general, interventions of the reviewed articles had favourable effects on function health of older adults. While physical activity has been identified as an important determinant of functional health, the ways to engage in and accumulate sufficient daily physical activity warrant investigation. It is also important to explore interventions which enhance daily, self-driven physical activity of elderly, as normally supervised physical activity bears higher costs

Fish bone foreign body presenting with an acute fulminating retropharyngeal abscess in a resource-challenged center: a case report

<p>Abstract</p> <p>Introduction</p> <p>A retropharyngeal abscess is a potentially life-threatening infection in the deep space of the neck, which can compromise the airway. Its management requires highly specialized care, including surgery and intensive care, to reduce mortality. This is the first case of a gas-forming abscess reported from this region, but not the first such report in the literature.</p> <p>Case presentation</p> <p>We present a case of a 16-month-old Yoruba baby girl with a gas-forming retropharyngeal abscess secondary to fish bone foreign body with laryngeal spasm that was managed in the recovery room. We highlight specific problems encountered in the management of this case in a resource-challenged center such as ours.</p> <p>Conclusion</p> <p>We describe an unusual presentation of a gas-forming organism causing a retropharyngeal abscess in a child. The patient's condition was treated despite the challenges of inadequate resources for its management. We recommend early recognition through adequate evaluation of any oropharyngeal injuries or infection and early referral to the specialist with prompt surgical intervention.</p

Growth factor-enriched autologous plasma improves wound healing after surgical debridement in odontogenic necrotizing fasciitis: a case report

<p>Abstract</p> <p>Background</p> <p>Odontogenic necrotizing fasciitis of the neck is a fulminant infection of odontogenic origin that quickly spreads along the fascial planes and results in necrosis of the affected tissues. It is usually polymicrobial, occurs frequently in immunocompromised patients, and has a high mortality rate.</p> <p>Case presentation</p> <p>A 69-year old Mexican male had a pain in the maxillar right-canine region and a swelling of the submental and submandibular regions. Our examination revealed local pain, tachycardia, hyperthermia (39°C), and the swelling of bilateral submental and submandibular regions, which also were erythematous, hyperthermic, crepitant, and with a positive Godet sign. Mobility and third-degree caries were seen in the right mandibular canine. Bacteriological cultures isolated <it>streptococcus pyogenes </it>and <it>staphylococcus aureus</it>. The histopathological diagnosis was odontogenic necrotizing fasciitis of the submental and submandibular regions. The initial treatment was surgical debridement and the administration of antibiotics. After cultures were negative, the surgical wound was treated with a growth factor-enriched autologous plasma eight times every third day until complete healing occurred.</p> <p>Conclusions</p> <p>The treatment with a growth factor-enriched autologous plasma caused a rapid healing of an extensive surgical wound in a patient with odontogenic necrotizing fasciitis. The benefits were rapid tissue regeneration, an aesthetic and a functional scar, and the avoidance of further surgery and possible complications.</p

Do we need to distance ourselves from the distance concept? Why home and host country context might matter more than (cultural) distance

We scrutinize the explanatory power of one of the key concepts in International Business: the concept of (cultural) distance. Here we focus on its effect on entry mode choice, one of the most researched fields in international business strategy. Our findings might, however, be equally be relevant for the field of International Business as a whole. Our analysis is based on a review of 92 prior studies on entry mode choice, as well as an empirical investigation in over 800 subsidiaries of MNCs, covering nine host and fifteen home countries across the world. We conclude that the explanatory power of distance is highly limited once home and host country context are accounted for, and that any significant effects of cultural distance on entry mode choice might simply be caused by inadequate sampling. Entry mode studies in particular, and International Business research in general, would do well to reconsider its fascination with distance measures, and instead, focus first and foremost on differences in home and host country context. We argue that serious engagement with deep contextualization is necessary in International Business research to pose new and relevant questions and develop new and innovative theories that explain empirical phenomena